/*		 
 * Copyright (C) 2002-2014 Sebastiano Vigna 
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *     http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License. 
 *
 *
 *
 * For the sorting and binary search code:
 *
 * Copyright (C) 1999 CERN - European Organization for Nuclear Research.
 *
 *   Permission to use, copy, modify, distribute and sell this software and
 *   its documentation for any purpose is hereby granted without fee,
 *   provided that the above copyright notice appear in all copies and that
 *   both that copyright notice and this permission notice appear in
 *   supporting documentation. CERN makes no representations about the
 *   suitability of this software for any purpose. It is provided "as is"
 *   without expressed or implied warranty. 
 */

package PACKAGE;

import it.unimi.dsi.fastutil.Arrays;
import it.unimi.dsi.fastutil.Hash;
import java.util.Random;

#if #keys(primitive)

/** A class providing static methods and objects that do useful things with type-specific arrays.
 *
 * <p>In particular, the <code>ensureCapacity()</code>, <code>grow()</code>,
 * <code>trim()</code> and <code>setLength()</code> methods allow to handle
 * arrays much like array lists. This can be very useful when efficiency (or
 * syntactic simplicity) reasons make array lists unsuitable.
 *
 * <P>Note that {@link it.unimi.dsi.fastutil.io.BinIO} and {@link it.unimi.dsi.fastutil.io.TextIO}
 * contain several methods make it possible to load and save arrays of primitive types as sequences
 * of elements in {@link java.io.DataInput} format (i.e., not as objects) or as sequences of lines of text.
 *
 * @see java.util.Arrays
 */

public class ARRAYS {

#else

import java.util.Comparator;

/** A class providing static methods and objects that do useful things with type-specific arrays.
 *
 * In particular, the <code>ensureCapacity()</code>, <code>grow()</code>,
 * <code>trim()</code> and <code>setLength()</code> methods allow to handle
 * arrays much like array lists. This can be very useful when efficiency (or
 * syntactic simplicity) reasons make array lists unsuitable.
 *
 * <P><strong>Warning:</strong> creating arrays 
 * using {@linkplain java.lang.reflect.Array#newInstance(Class,int) reflection}, as it
 * happens in {@link #ensureCapacity(Object[],int,int)} and {@link #grow(Object[],int,int)},
 * is <em>significantly slower</em> than using <code>new</code>. This phenomenon is particularly
 * evident in the first growth phases of an array reallocated with doubling (or similar) logic.
 *
 * @see java.util.Arrays
 */

public class ARRAYS {

#endif
	private ARRAYS() {}

	/** A static, final, empty array. */
	public final static KEY_TYPE[] EMPTY_ARRAY = {};


#if #keyclass(Object)
	/** Creates a new array using a the given one as prototype. 
	 *
	 * <P>This method returns a new array of the given length whose element
	 * are of the same class as of those of <code>prototype</code>. In case
	 * of an empty array, it tries to return {@link #EMPTY_ARRAY}, if possible.
	 *
	 * @param prototype an array that will be used to type the new one.
	 * @param length the length of the new array.
	 * @return a new array of given type and length.
	 */

	@SuppressWarnings("unchecked")
	private static <K> K[] newArray( final K[] prototype, final int length ) {
		final Class<?> componentType = prototype.getClass().getComponentType();
		if ( length == 0 && componentType == Object.class ) return (K[])EMPTY_ARRAY;
		return (K[])java.lang.reflect.Array.newInstance( prototype.getClass().getComponentType(), length );
	}
#endif

	/** Ensures that an array can contain the given number of entries.
	 *
	 * <P>If you cannot foresee whether this array will need again to be
	 * enlarged, you should probably use <code>grow()</code> instead.
	 *
	 * @param array an array.
	 * @param length the new minimum length for this array.
	 * @return <code>array</code>, if it contains <code>length</code> entries or more; otherwise,
	 * an array with <code>length</code> entries whose first <code>array.length</code>
	 * entries are the same as those of <code>array</code>.
	 */
	public static KEY_GENERIC KEY_GENERIC_TYPE[] ensureCapacity( final KEY_GENERIC_TYPE[] array, final int length ) {
		if ( length > array.length ) {
			final KEY_GENERIC_TYPE t[] =
#if #keyclass(Object)
				newArray( array, length );
#else
				new KEY_TYPE[ length ];
#endif
			System.arraycopy( array, 0, t, 0, array.length );
			return t;
		}
		return array;
	}

	/** Ensures that an array can contain the given number of entries, preserving just a part of the array.
	 *
	 * @param array an array.
	 * @param length the new minimum length for this array.
	 * @param preserve the number of elements of the array that must be preserved in case a new allocation is necessary.
	 * @return <code>array</code>, if it can contain <code>length</code> entries or more; otherwise,
	 * an array with <code>length</code> entries whose first <code>preserve</code>
	 * entries are the same as those of <code>array</code>.
	 */
	public static KEY_GENERIC KEY_GENERIC_TYPE[] ensureCapacity( final KEY_GENERIC_TYPE[] array, final int length, final int preserve ) {
		if ( length > array.length ) {
			final KEY_GENERIC_TYPE t[] =
#if #keyclass(Object)
				newArray( array, length );
#else
				new KEY_TYPE[ length ];
#endif
			System.arraycopy( array, 0, t, 0, preserve );
			return t;
		}
		return array;
	}

	/** Grows the given array to the maximum between the given length and
	 * the current length multiplied by two, provided that the given
	 * length is larger than the current length.
	 *
	 * <P>If you want complete control on the array growth, you
	 * should probably use <code>ensureCapacity()</code> instead.
	 *
	 * @param array an array.
	 * @param length the new minimum length for this array.
	 * @return <code>array</code>, if it can contain <code>length</code>
	 * entries; otherwise, an array with
	 * max(<code>length</code>,<code>array.length</code>/&phi;) entries whose first
	 * <code>array.length</code> entries are the same as those of <code>array</code>.
	 * */

	public static KEY_GENERIC KEY_GENERIC_TYPE[] grow( final KEY_GENERIC_TYPE[] array, final int length ) {
		if ( length > array.length ) {
			final int newLength = (int)Math.max( Math.min( 2L * array.length, Arrays.MAX_ARRAY_SIZE ), length );
			final KEY_GENERIC_TYPE t[] =
#if #keyclass(Object)
				newArray( array, newLength );
#else
				new KEY_TYPE[ newLength ];
#endif
			System.arraycopy( array, 0, t, 0, array.length );
			return t;
		}
		return array;
	}

	/** Grows the given array to the maximum between the given length and
	 * the current length multiplied by two, provided that the given
	 * length is larger than the current length, preserving just a part of the array.
	 *
	 * <P>If you want complete control on the array growth, you
	 * should probably use <code>ensureCapacity()</code> instead.
	 *
	 * @param array an array.
	 * @param length the new minimum length for this array.
	 * @param preserve the number of elements of the array that must be preserved in case a new allocation is necessary.
	 * @return <code>array</code>, if it can contain <code>length</code>
	 * entries; otherwise, an array with
	 * max(<code>length</code>,<code>array.length</code>/&phi;) entries whose first
	 * <code>preserve</code> entries are the same as those of <code>array</code>.
	 * */

	public static KEY_GENERIC KEY_GENERIC_TYPE[] grow( final KEY_GENERIC_TYPE[] array, final int length, final int preserve ) {

		if ( length > array.length ) {
			final int newLength = (int)Math.max( Math.min( 2L * array.length, Arrays.MAX_ARRAY_SIZE ), length );

			final KEY_GENERIC_TYPE t[] =
#if #keyclass(Object)
				newArray( array, newLength );
#else
				new KEY_TYPE[ newLength ];
#endif
			System.arraycopy( array, 0, t, 0, preserve );

			return t;
		}
		return array;

	}

	/** Trims the given array to the given length.
	 *
	 * @param array an array.
	 * @param length the new maximum length for the array.
	 * @return <code>array</code>, if it contains <code>length</code>
	 * entries or less; otherwise, an array with
	 * <code>length</code> entries whose entries are the same as
	 * the first <code>length</code> entries of <code>array</code>.
	 * 
	 */

	public static KEY_GENERIC KEY_GENERIC_TYPE[] trim( final KEY_GENERIC_TYPE[] array, final int length ) {
		if ( length >= array.length ) return array;
		final KEY_GENERIC_TYPE t[] =
#if #keyclass(Object)
			newArray( array, length );
#else
			length == 0 ? EMPTY_ARRAY : new KEY_TYPE[ length ];
#endif
		System.arraycopy( array, 0, t, 0, length );
		return t;
	}

	/** Sets the length of the given array.
	 *
	 * @param array an array.
	 * @param length the new length for the array.
	 * @return <code>array</code>, if it contains exactly <code>length</code>
	 * entries; otherwise, if it contains <em>more</em> than
	 * <code>length</code> entries, an array with <code>length</code> entries
	 * whose entries are the same as the first <code>length</code> entries of
	 * <code>array</code>; otherwise, an array with <code>length</code> entries
	 * whose first <code>array.length</code> entries are the same as those of
	 * <code>array</code>.
	 * 
	 */

	public static KEY_GENERIC KEY_GENERIC_TYPE[] setLength( final KEY_GENERIC_TYPE[] array, final int length ) {
		if ( length == array.length ) return array;
		if ( length < array.length ) return trim( array, length );
		return ensureCapacity( array, length );
	}

	/** Returns a copy of a portion of an array.
	 *
	 * @param array an array.
	 * @param offset the first element to copy.
	 * @param length the number of elements to copy.
	 * @return a new array containing <code>length</code> elements of <code>array</code> starting at <code>offset</code>.
	 */

	public static KEY_GENERIC KEY_GENERIC_TYPE[] copy( final KEY_GENERIC_TYPE[] array, final int offset, final int length ) {
		ensureOffsetLength( array, offset, length );
		final KEY_GENERIC_TYPE[] a = 
#if #keyclass(Object)
			newArray( array, length );
#else
			length == 0 ? EMPTY_ARRAY : new KEY_TYPE[ length ];
#endif
		System.arraycopy( array, offset, a, 0, length );
		return a;
	}

	/** Returns a copy of an array.
	 *
	 * @param array an array.
	 * @return a copy of <code>array</code>.
	 */

	public static KEY_GENERIC KEY_GENERIC_TYPE[] copy( final KEY_GENERIC_TYPE[] array ) {
		return array.clone();
	}

	/** Fills the given array with the given value.
	 *
	 * <P>This method uses a backward loop. It is significantly faster than the corresponding
	 * method in {@link java.util.Arrays}.
	 *
	 * @param array an array.
	 * @param value the new value for all elements of the array.
	 */

	public static KEY_GENERIC void fill( final KEY_GENERIC_TYPE[] array, final KEY_GENERIC_TYPE value ) {
		int i = array.length;
		while( i-- != 0 ) array[ i ] = value;
	}

	/** Fills a portion of the given array with the given value.
	 *
	 * <P>If possible (i.e., <code>from</code> is 0) this method uses a
	 * backward loop. In this case, it is significantly faster than the
	 * corresponding method in {@link java.util.Arrays}.
	 *
	 * @param array an array.
	 * @param from the starting index of the portion to fill (inclusive).
	 * @param to the end index of the portion to fill (exclusive).
	 * @param value the new value for all elements of the specified portion of the array.
	 */

	public static KEY_GENERIC void fill( final KEY_GENERIC_TYPE[] array, final int from, int to, final KEY_GENERIC_TYPE value ) {
		ensureFromTo( array, from, to );
		if ( from == 0 ) while( to-- != 0 ) array[ to ] = value;
		else for( int i = from; i < to; i++ ) array[ i ] = value;
	}



	/** Returns true if the two arrays are elementwise equal.
	 *
	 * @param a1 an array.
	 * @param a2 another array.
	 * @return true if the two arrays are of the same length, and their elements are equal.
	 * @deprecated Please use the corresponding {@link java.util.Arrays} method, which is intrinsified in recent JVMs.
	 */

	@Deprecated
	public static KEY_GENERIC boolean equals( final KEY_GENERIC_TYPE[] a1, final KEY_GENERIC_TYPE a2[] ) {
		int i = a1.length;
		if ( i != a2.length ) return false;
		while( i-- != 0 ) if (! KEY_EQUALS( a1[ i ], a2[ i ] ) ) return false;
		return true;
	}




	/** Ensures that a range given by its first (inclusive) and last (exclusive) elements fits an array.
	 *
	 * <P>This method may be used whenever an array range check is needed.
	 *
	 * @param a an array.
	 * @param from a start index (inclusive).
	 * @param to an end index (exclusive).
	 * @throws IllegalArgumentException if <code>from</code> is greater than <code>to</code>.
	 * @throws ArrayIndexOutOfBoundsException if <code>from</code> or <code>to</code> are greater than the array length or negative.
	 */
	public static KEY_GENERIC void ensureFromTo( final KEY_GENERIC_TYPE[] a, final int from, final int to ) {
		Arrays.ensureFromTo( a.length, from, to );
	}

	/** Ensures that a range given by an offset and a length fits an array.
	 *
	 * <P>This method may be used whenever an array range check is needed.
	 *
	 * @param a an array.
	 * @param offset a start index.
	 * @param length a length (the number of elements in the range).
	 * @throws IllegalArgumentException if <code>length</code> is negative.
	 * @throws ArrayIndexOutOfBoundsException if <code>offset</code> is negative or <code>offset</code>+<code>length</code> is greater than the array length.
	 */
	public static KEY_GENERIC void ensureOffsetLength( final KEY_GENERIC_TYPE[] a, final int offset, final int length ) {
		Arrays.ensureOffsetLength( a.length, offset, length );
	}

	private static final int SMALL = 7;
	private static final int MEDIUM = 50;

	private static KEY_GENERIC void swap( final KEY_GENERIC_TYPE x[], final int a, final int b ) {
		final KEY_GENERIC_TYPE t = x[ a ];
		x[ a ] = x[ b ];
		x[ b ] = t;
	}

	private static KEY_GENERIC void vecSwap( final KEY_GENERIC_TYPE[] x, int a, int b, final int n ) {
		for( int i = 0; i < n; i++, a++, b++ ) swap( x, a, b );
	}
 
	private static KEY_GENERIC int med3( final KEY_GENERIC_TYPE x[], final int a, final int b, final int c, KEY_COMPARATOR KEY_GENERIC comp ) {
		int ab = comp.compare( x[ a ], x[ b ] );
		int ac = comp.compare( x[ a ], x[ c ] );
		int bc = comp.compare( x[ b ], x[ c ] );
		return ( ab < 0 ?
			( bc < 0 ? b : ac < 0 ? c : a ) :
			( bc > 0 ? b : ac > 0 ? c : a ) );
	}


	private static KEY_GENERIC void selectionSort( final KEY_GENERIC_TYPE[] a, final int from, final int to, final KEY_COMPARATOR KEY_GENERIC comp ) {
		for( int i = from; i < to - 1; i++ ) {
			int m = i;
			for( int j = i + 1; j < to; j++ ) if ( comp.compare( a[ j ], a[ m ] ) < 0 ) m = j;
			if ( m != i ) {
				final KEY_GENERIC_TYPE u = a[ i ];
				a[ i ] = a[ m ];
				a[ m ] = u;
			}
		}
	}


	private static KEY_GENERIC void insertionSort( final KEY_GENERIC_TYPE[] a, final int from, final int to, final KEY_COMPARATOR KEY_GENERIC comp  ) {
		for ( int i = from; ++i < to; ) { 
			KEY_GENERIC_TYPE t = a[ i ];
			int j = i;
			for ( KEY_GENERIC_TYPE u = a[ j - 1 ]; comp.compare( t, u ) < 0; u = a[ --j - 1 ] ) {
				a[ j ] = u;
				if ( from == j - 1 ) {
					--j;
					break;
				}
			}
			a[ j ] = t;
		}
	}

	@SuppressWarnings("unchecked")
	private static KEY_GENERIC void selectionSort( final KEY_GENERIC_TYPE[] a, final int from, final int to ) {
		for( int i = from; i < to - 1; i++ ) {
			int m = i;
			for( int j = i + 1; j < to; j++ ) if ( KEY_LESS( a[ j ], a[ m ] ) ) m = j;
			if ( m != i ) {
				final KEY_GENERIC_TYPE u = a[ i ];
				a[ i ] = a[ m ];
				a[ m ] = u;
			}
		}
	}
	
	@SuppressWarnings("unchecked")
	private static KEY_GENERIC void insertionSort( final KEY_GENERIC_TYPE[] a, final int from, final int to ) {
		for ( int i = from; ++i < to; ) { 
			KEY_GENERIC_TYPE t = a[ i ];
			int j = i;
			for ( KEY_GENERIC_TYPE u = a[ j - 1 ]; KEY_LESS( t, u ); u = a[ --j - 1 ] ) {
				a[ j ] = u;
				if ( from == j - 1 ) {
					--j;
					break;
				}
			}
			a[ j ] = t;
		}
	}


	/** Sorts the specified range of elements according to the order induced by the specified
	 * comparator using quicksort. 
	 * 
	 * <p>The sorting algorithm is a tuned quicksort adapted from Jon L. Bentley and M. Douglas
	 * McIlroy, &ldquo;Engineering a Sort Function&rdquo;, <i>Software: Practice and Experience</i>, 23(11), pages
	 * 1249&minus;1265, 1993.
	 *
	 * <p>Note that this implementation does not allocate any object, contrarily to the implementation
	 * used to sort primitive types in {@link java.util.Arrays}, which switches to mergesort on large inputs.
	 * 
	 * @param x the array to be sorted.
	 * @param from the index of the first element (inclusive) to be sorted.
	 * @param to the index of the last element (exclusive) to be sorted.
	 * @param comp the comparator to determine the sorting order.
	 * 
	 */
	public static KEY_GENERIC void quickSort( final KEY_GENERIC_TYPE[] x, final int from, final int to, final KEY_COMPARATOR KEY_GENERIC comp ) {
		final int len = to - from;
		
		// Selection sort on smallest arrays
		if ( len < SMALL ) {
			selectionSort( x, from, to, comp );
			return;
		}

		// Choose a partition element, v
		int m = from + len / 2;	 // Small arrays, middle element
		if ( len > SMALL ) {
			int l = from;
			int n = to - 1;
			if ( len > MEDIUM ) {		// Big arrays, pseudomedian of 9
				int s = len / 8;
				l = med3( x, l, l + s, l + 2 * s, comp );
				m = med3( x, m - s, m, m + s, comp );
				n = med3( x, n - 2 * s, n - s, n, comp );
			}
			m = med3( x, l, m, n, comp ); // Mid-size, med of 3
		}
		
		final KEY_GENERIC_TYPE v = x[ m ];

		// Establish Invariant: v* (<v)* (>v)* v*
		int a = from, b = a, c = to - 1, d = c;
		while(true) {
			int comparison;
			while ( b <= c && ( comparison = comp.compare( x[ b ], v ) ) <= 0 ) {
				if ( comparison == 0 ) swap( x, a++, b );
				b++;
			}
			while (c >= b && ( comparison = comp.compare( x[ c ], v ) ) >=0 ) {
				if ( comparison == 0 ) swap( x, c, d-- );
				c--;
			}
			if ( b > c ) break;
			swap( x, b++, c-- );
		}

		// Swap partition elements back to middle
		int s, n = to;
		s = Math.min( a - from, b - a );
		vecSwap( x, from, b - s, s );
		s = Math.min( d - c, n - d - 1 );
		vecSwap( x, b, n - s, s );

		// Recursively sort non-partition-elements
		if ( ( s = b - a ) > 1 ) quickSort( x, from, from + s, comp );
		if ( ( s = d - c ) > 1 ) quickSort( x, n - s, n, comp );

	}

	/** Sorts an array according to the order induced by the specified
	 * comparator using quicksort. 
	 * 
	 * <p>The sorting algorithm is a tuned quicksort adapted from Jon L. Bentley and M. Douglas
	 * McIlroy, &ldquo;Engineering a Sort Function&rdquo;, <i>Software: Practice and Experience</i>, 23(11), pages
	 * 1249&minus;1265, 1993.
	 * 
	 * <p>Note that this implementation does not allocate any object, contrarily to the implementation
	 * used to sort primitive types in {@link java.util.Arrays}, which switches to mergesort on large inputs.
	 * 
	 * @param x the array to be sorted.
	 * @param comp the comparator to determine the sorting order.
	 * 
	 */
	public static KEY_GENERIC void quickSort( final KEY_GENERIC_TYPE[] x, final KEY_COMPARATOR KEY_GENERIC comp ) {
		quickSort( x, 0, x.length, comp );	
	}
	

	@SuppressWarnings("unchecked")
	private static KEY_GENERIC int med3( final KEY_GENERIC_TYPE x[], final int a, final int b, final int c ) {
		int ab = KEY_CMP( x[ a ], x[ b ] );
		int ac = KEY_CMP( x[ a ], x[ c ] );
		int bc = KEY_CMP( x[ b ], x[ c ] );
		return ( ab < 0 ?
			( bc < 0 ? b : ac < 0 ? c : a ) :
			( bc > 0 ? b : ac > 0 ? c : a ) );
	}


	/** Sorts the specified range of elements according to the natural ascending order using quicksort.
	 * 
	 * <p>The sorting algorithm is a tuned quicksort adapted from Jon L. Bentley and M. Douglas
	 * McIlroy, &ldquo;Engineering a Sort Function&rdquo;, <i>Software: Practice and Experience</i>, 23(11), pages
	 * 1249&minus;1265, 1993.
	 * 
	 * <p>Note that this implementation does not allocate any object, contrarily to the implementation
	 * used to sort primitive types in {@link java.util.Arrays}, which switches to mergesort on large inputs.
	 * 
	 * @param x the array to be sorted.
	 * @param from the index of the first element (inclusive) to be sorted.
	 * @param to the index of the last element (exclusive) to be sorted.
	 */

	@SuppressWarnings("unchecked")
	public static KEY_GENERIC void quickSort( final KEY_GENERIC_TYPE[] x, final int from, final int to ) {
		final int len = to - from;

		// Selection sort on smallest arrays
		if ( len < SMALL ) {
			selectionSort( x, from, to );
			return;
		}

		// Choose a partition element, v
		int m = from + len / 2;	 // Small arrays, middle element
		if ( len > SMALL ) {
			int l = from;
			int n = to - 1;
			if ( len > MEDIUM ) {		// Big arrays, pseudomedian of 9
				int s = len / 8;
				l = med3( x, l, l + s, l + 2 * s );
				m = med3( x, m - s, m, m + s );
				n = med3( x, n - 2 * s, n - s, n );
			}
			m = med3( x, l, m, n ); // Mid-size, med of 3
		}
		
		final KEY_GENERIC_TYPE v = x[ m ];

		// Establish Invariant: v* (<v)* (>v)* v*
		int a = from, b = a, c = to - 1, d = c;
		while(true) {
			int comparison;
			while ( b <= c && ( comparison = KEY_CMP( x[ b ], v ) ) <= 0 ) {
				if ( comparison == 0 ) swap( x, a++, b );
				b++;
			}
			while (c >= b && ( comparison = KEY_CMP( x[ c ], v ) ) >=0 ) {
				if ( comparison == 0 ) swap( x, c, d-- );
				c--;
			}
			if ( b > c ) break;
			swap( x, b++, c-- );
		}

		// Swap partition elements back to middle
		int s, n = to;
		s = Math.min( a - from, b - a );
		vecSwap( x, from, b - s, s );
		s = Math.min( d - c, n - d - 1 );
		vecSwap( x, b, n - s, s );

		// Recursively sort non-partition-elements
		if ( ( s = b - a ) > 1 ) quickSort( x, from, from + s );
		if ( ( s = d - c ) > 1 ) quickSort( x, n - s, n );

	}

	/** Sorts an array according to the natural ascending order using quicksort.
	 * 
	 * <p>The sorting algorithm is a tuned quicksort adapted from Jon L. Bentley and M. Douglas
	 * McIlroy, &ldquo;Engineering a Sort Function&rdquo;, <i>Software: Practice and Experience</i>, 23(11), pages
	 * 1249&minus;1265, 1993.
	 * 
	 * <p>Note that this implementation does not allocate any object, contrarily to the implementation
	 * used to sort primitive types in {@link java.util.Arrays}, which switches to mergesort on large inputs.
	 * 
	 * @param x the array to be sorted.
	 * 
	 */
	public static KEY_GENERIC void quickSort( final KEY_GENERIC_TYPE[] x ) {
		quickSort( x, 0, x.length );	
	}
	
	/** Sorts the specified range of elements according to the natural ascending order using mergesort, using a given pre-filled support array.
	 * 
	 * <p>This sort is guaranteed to be <i>stable</i>: equal elements will not be reordered as a result
	 * of the sort. Moreover, no support arrays will be allocated. 
	 
	 * @param a the array to be sorted.
	 * @param from the index of the first element (inclusive) to be sorted.
	 * @param to the index of the last element (exclusive) to be sorted.
	 * @param supp a support array containing at least <code>to</code> elements, and whose entries are identical to those
	 * of {@code a} in the specified range.
	 */

	@SuppressWarnings("unchecked")
	public static KEY_GENERIC void mergeSort( final KEY_GENERIC_TYPE a[], final int from, final int to, final KEY_GENERIC_TYPE supp[] ) {
		int len = to - from;
		
		// Insertion sort on smallest arrays
		if ( len < SMALL ) {
			insertionSort( a, from, to );
			return;
		}
	
		// Recursively sort halves of a into supp
		final int mid = ( from + to ) >>> 1;
		mergeSort( supp, from, mid, a );
		mergeSort( supp, mid, to, a );
	
		// If list is already sorted, just copy from supp to a.  This is an
		// optimization that results in faster sorts for nearly ordered lists.
		if ( KEY_LESSEQ( supp[ mid - 1 ], supp[ mid ] ) ) {
			System.arraycopy( supp, from, a, from, len );
			return;
		}
	
		// Merge sorted halves (now in supp) into a
		for( int i = from, p = from, q = mid; i < to; i++ ) {
			if ( q >= to || p < mid && KEY_LESSEQ( supp[ p ], supp[ q ] ) ) a[ i ] = supp[ p++ ];
			else a[ i ] = supp[ q++ ];
		}
	}

	/** Sorts the specified range of elements according to the natural ascending order using mergesort.
	 * 
	 * <p>This sort is guaranteed to be <i>stable</i>: equal elements will not be reordered as a result
	 * of the sort. An array as large as <code>a</code> will be allocated by this method.
	 
	 * @param a the array to be sorted.
	 * @param from the index of the first element (inclusive) to be sorted.
	 * @param to the index of the last element (exclusive) to be sorted.
	 */
	public static KEY_GENERIC void mergeSort( final KEY_GENERIC_TYPE a[], final int from, final int to ) {
		mergeSort( a, from, to, a.clone() );
	}

	/**	Sorts an array according to the natural ascending order using mergesort.
	 * 
	 * <p>This sort is guaranteed to be <i>stable</i>: equal elements will not be reordered as a result
	 * of the sort. An array as large as <code>a</code> will be allocated by this method.
	 
	 * @param a the array to be sorted.
	 */
	public static KEY_GENERIC void mergeSort( final KEY_GENERIC_TYPE a[] ) {
		mergeSort( a, 0, a.length );
	}

	/** Sorts the specified range of elements according to the order induced by the specified
	 * comparator using mergesort, using a given pre-filled support array.
	 * 
	 * <p>This sort is guaranteed to be <i>stable</i>: equal elements will not be reordered as a result
	 * of the sort. Moreover, no support arrays will be allocated.
	 
	 * @param a the array to be sorted.
	 * @param from the index of the first element (inclusive) to be sorted.
	 * @param to the index of the last element (exclusive) to be sorted.
	 * @param comp the comparator to determine the sorting order.
	 * @param supp a support array containing at least <code>to</code> elements, and whose entries are identical to those
	 * of {@code a} in the specified range.
	 */
	@SuppressWarnings("unchecked")
	public static KEY_GENERIC void mergeSort( final KEY_GENERIC_TYPE a[], final int from, final int to, KEY_COMPARATOR KEY_GENERIC comp, final KEY_GENERIC_TYPE supp[] ) {
		int len = to - from;
		
		// Insertion sort on smallest arrays
		if ( len < SMALL ) {
			insertionSort( a, from, to, comp );
			return;
    	}
	
		// Recursively sort halves of a into supp
		final int mid = ( from + to ) >>> 1;
		mergeSort( supp, from, mid, comp, a );
		mergeSort( supp, mid, to, comp, a );
	
		// If list is already sorted, just copy from supp to a.  This is an
		// optimization that results in faster sorts for nearly ordered lists.
		if ( comp.compare( supp[ mid - 1 ], supp[ mid ] ) <= 0 ) {
			System.arraycopy( supp, from, a, from, len );
			return;
		}
	
		// Merge sorted halves (now in supp) into a
		for( int i = from, p = from, q = mid; i < to; i++ ) {
			if ( q >= to || p < mid && comp.compare( supp[ p ], supp[ q ] ) <= 0 ) a[ i ] = supp[ p++ ];
			else a[ i ] = supp[ q++ ];
		}
	}

	/** Sorts the specified range of elements according to the order induced by the specified
	 * comparator using mergesort.
	 * 
	 * <p>This sort is guaranteed to be <i>stable</i>: equal elements will not be reordered as a result
	 * of the sort. An array as large as <code>a</code> will be allocated by this method.
	 *
	 * @param a the array to be sorted.
	 * @param from the index of the first element (inclusive) to be sorted.
	 * @param to the index of the last element (exclusive) to be sorted.
	 * @param comp the comparator to determine the sorting order.
	 */
	public static KEY_GENERIC void mergeSort( final KEY_GENERIC_TYPE a[], final int from, final int to, KEY_COMPARATOR KEY_GENERIC comp ) {
		mergeSort( a, from, to, comp, a.clone() );
	}

	/** Sorts an array according to the order induced by the specified
	 * comparator using mergesort.
	 * 
	 * <p>This sort is guaranteed to be <i>stable</i>: equal elements will not be reordered as a result
	 * of the sort.  An array as large as <code>a</code> will be allocated by this method.
	 
	 * @param a the array to be sorted.
	 * @param comp the comparator to determine the sorting order.
	 */
	public static KEY_GENERIC void mergeSort( final KEY_GENERIC_TYPE a[], KEY_COMPARATOR KEY_GENERIC comp ) {
		mergeSort( a, 0, a.length, comp );
	}

#if ! #keyclass(Boolean)

	/**
	 * Searches a range of the specified array for the specified value using 
	 * the binary search algorithm. The range must be sorted prior to making this call. 
	 * If it is not sorted, the results are undefined. If the range contains multiple elements with 
	 * the specified value, there is no guarantee which one will be found.
	 *
	 * @param a the array to be searched.
	 * @param from  the index of the first element (inclusive) to be searched.
	 * @param to  the index of the last element (exclusive) to be searched.
	 * @param key the value to be searched for.
	 * @return index of the search key, if it is contained in the array;
	 *             otherwise, <samp>(-(<i>insertion point</i>) - 1)</samp>.  The <i>insertion
	 *             point</i> is defined as the the point at which the value would
	 *             be inserted into the array: the index of the first
	 *             element greater than the key, or the length of the array, if all
	 *             elements in the array are less than the specified key.  Note
	 *             that this guarantees that the return value will be &gt;= 0 if
	 *             and only if the key is found.
	 * @see java.util.Arrays
	 */
	@SuppressWarnings({"unchecked","rawtypes"})
	public static KEY_GENERIC int binarySearch( final KEY_GENERIC_TYPE[] a, int from, int to, final KEY_GENERIC_TYPE key ) {
		KEY_GENERIC_TYPE midVal;
		to--;
		while (from <= to) {
			final int mid = (from + to) >>> 1;
			midVal = a[ mid ];
#if #keys(primitive)
			if (midVal < key) from = mid + 1;
			else if (midVal > key) to = mid - 1;
			else return mid;
#else
			final int cmp = ((Comparable)midVal).compareTo( key );
			if ( cmp < 0 ) from = mid + 1;
			else if (cmp > 0) to = mid - 1;
			else return mid;
#endif
        }
		return -( from + 1 );
	}

	/**
	 * Searches an array for the specified value using 
	 * the binary search algorithm. The range must be sorted prior to making this call. 
	 * If it is not sorted, the results are undefined. If the range contains multiple elements with 
	 * the specified value, there is no guarantee which one will be found.
	 *
	 * @param a the array to be searched.
	 * @param key the value to be searched for.
	 * @return index of the search key, if it is contained in the array;
	 *             otherwise, <samp>(-(<i>insertion point</i>) - 1)</samp>.  The <i>insertion
	 *             point</i> is defined as the the point at which the value would
	 *             be inserted into the array: the index of the first
	 *             element greater than the key, or the length of the array, if all
	 *             elements in the array are less than the specified key.  Note
	 *             that this guarantees that the return value will be &gt;= 0 if
	 *             and only if the key is found.
	 * @see java.util.Arrays
	 */
	public static KEY_GENERIC int binarySearch( final KEY_GENERIC_TYPE[] a, final KEY_GENERIC_TYPE key ) {
		return binarySearch( a, 0, a.length, key );
	}

	/**
	 * Searches a range of the specified array for the specified value using 
	 * the binary search algorithm and a specified comparator. The range must be sorted following the comparator prior to making this call. 
	 * If it is not sorted, the results are undefined. If the range contains multiple elements with 
	 * the specified value, there is no guarantee which one will be found.
	 *
	 * @param a the array to be searched.
	 * @param from  the index of the first element (inclusive) to be searched.
	 * @param to  the index of the last element (exclusive) to be searched.
	 * @param key the value to be searched for.
	 * @param c a comparator.
	 * @return index of the search key, if it is contained in the array;
	 *             otherwise, <samp>(-(<i>insertion point</i>) - 1)</samp>.  The <i>insertion
	 *             point</i> is defined as the the point at which the value would
	 *             be inserted into the array: the index of the first
	 *             element greater than the key, or the length of the array, if all
	 *             elements in the array are less than the specified key.  Note
	 *             that this guarantees that the return value will be &gt;= 0 if
	 *             and only if the key is found.
	 * @see java.util.Arrays
	 */
	public static KEY_GENERIC int binarySearch( final KEY_GENERIC_TYPE[] a, int from, int to, final KEY_GENERIC_TYPE key, final KEY_COMPARATOR KEY_GENERIC c ) {
		KEY_GENERIC_TYPE midVal;
		to--;
		while (from <= to) {
			final int mid = (from + to) >>> 1;
			midVal = a[ mid ];
			final int cmp = c.compare( midVal, key );
			if ( cmp < 0 ) from = mid + 1;
			else if (cmp > 0) to = mid - 1;
			else return mid; // key found
		}
		return -( from + 1 );
	}

	/**
	 * Searches an array for the specified value using 
	 * the binary search algorithm and a specified comparator. The range must be sorted following the comparator prior to making this call. 
	 * If it is not sorted, the results are undefined. If the range contains multiple elements with 
	 * the specified value, there is no guarantee which one will be found.
	 *
	 * @param a the array to be searched.
	 * @param key the value to be searched for.
	 * @param c a comparator.
	 * @return index of the search key, if it is contained in the array;
	 *             otherwise, <samp>(-(<i>insertion point</i>) - 1)</samp>.  The <i>insertion
	 *             point</i> is defined as the the point at which the value would
	 *             be inserted into the array: the index of the first
	 *             element greater than the key, or the length of the array, if all
	 *             elements in the array are less than the specified key.  Note
	 *             that this guarantees that the return value will be &gt;= 0 if
	 *             and only if the key is found.
	 * @see java.util.Arrays
	 */
	public static KEY_GENERIC int binarySearch( final KEY_GENERIC_TYPE[] a, final KEY_GENERIC_TYPE key, final KEY_COMPARATOR KEY_GENERIC c ) {
		return binarySearch( a, 0, a.length, key, c );
	}


#if #keys(primitive)
	/** The size of a digit used during radix sort (must be a power of 2). */
	private static final int DIGIT_BITS = 8;
	/** The mask to extract a digit of {@link #DIGIT_BITS} bits. */
	private static final int DIGIT_MASK = ( 1 << DIGIT_BITS ) - 1;
	/** The number of digits per element. */
	private static final int DIGITS_PER_ELEMENT = KEY_CLASS.SIZE / DIGIT_BITS;

	/** This method fixes negative numbers so that the combination exponent/significand is lexicographically sorted. */
#if #keyclass(Double)
	private static final long fixDouble( final double d ) {
		final long l = Double.doubleToLongBits( d );
		return l >= 0 ? l : l ^ 0x7FFFFFFFFFFFFFFFL;
	}	   
#elif #keyclass(Float)
	private static final long fixFloat( final float f ) {
		final long i = Float.floatToIntBits( f );
		return i >= 0 ? i : i ^ 0x7FFFFFFF;
	}
#endif


	/** Sorts the specified array using radix sort.
	 * 
	 * <p>The sorting algorithm is a tuned radix sort adapted from Peter M. McIlroy, Keith Bostic and M. Douglas
	 * McIlroy, &ldquo;Engineering radix sort&rdquo;, <i>Computing Systems</i>, 6(1), pages 5&minus;27 (1993),
	 * and further improved using the digit-oracle idea described by
	 * Juha K&auml;rkk&auml;inen and Tommi Rantala in &ldquo;Engineering radix sort for strings&rdquo;,
	 * <i>String Processing and Information Retrieval, 15th International Symposium</i>, volume 5280 of
	 * Lecture Notes in Computer Science, pages 3&minus;14, Springer (2008).
	 *
	 * <p>This implementation is significantly faster than quicksort 
	 * already at small sizes (say, more than 10000 elements), but it can only
	 * sort in ascending order. 
	 * It will allocate a support array of bytes with the same number of elements as the array to be sorted.
	 * 
	 * @param a the array to be sorted.
	 */
	public static void radixSort( final KEY_TYPE[] a ) {
		radixSort( a, 0, a.length );
	}

	/** Sorts the specified array using radix sort.
	 * 
	 * <p>The sorting algorithm is a tuned radix sort adapted from Peter M. McIlroy, Keith Bostic and M. Douglas
	 * McIlroy, &ldquo;Engineering radix sort&rdquo;, <i>Computing Systems</i>, 6(1), pages 5&minus;27 (1993),
	 * and further improved using the digit-oracle idea described by
	 * Juha K&auml;rkk&auml;inen and Tommi Rantala in &ldquo;Engineering radix sort for strings&rdquo;,
	 * <i>String Processing and Information Retrieval, 15th International Symposium</i>, volume 5280 of
	 * Lecture Notes in Computer Science, pages 3&minus;14, Springer (2008).
	 *
	 * <p>This implementation is significantly faster than quicksort 
	 * already at small sizes (say, more than 10000 elements), but it can only
	 * sort in ascending order. 
	 * It will allocate a support array of bytes with the same number of elements as the array to be sorted.
	 * 
	 * @param a the array to be sorted.
	 * @param from the index of the first element (inclusive) to be sorted.
	 * @param to the index of the last element (exclusive) to be sorted.
	 */
	public static void radixSort( final KEY_TYPE[] a, final int from, final int to ) {
		final int maxLevel = DIGITS_PER_ELEMENT - 1;

		final int stackSize = ( ( 1 << DIGIT_BITS ) - 1 ) * ( DIGITS_PER_ELEMENT - 1 ) + 1;
		final int[] offsetStack = new int[ stackSize ];
		int offsetPos = 0;
		final int[] lengthStack = new int[ stackSize ];
		int lengthPos = 0;
		final int[] levelStack = new int[ stackSize ];
		int levelPos = 0;
		
		offsetStack[ offsetPos++ ] = from;
		lengthStack[ lengthPos++ ] = to - from;
		levelStack[ levelPos++ ] = 0;

		final int[] count = new int[ 1 << DIGIT_BITS ];
		final int[] pos = new int[ 1 << DIGIT_BITS ];
		final byte[] digit = new byte[ to - from ];

		while( offsetPos > 0 ) {
			final int first = offsetStack[ --offsetPos ];
			final int length = lengthStack[ --lengthPos ];
			final int level = levelStack[ --levelPos ];
#if #keyclass(Character)
			final int signMask = 0;
#else
			final int signMask = level % DIGITS_PER_ELEMENT == 0 ? 1 << DIGIT_BITS - 1 : 0;
#endif
			
			if ( length < MEDIUM ) {
				selectionSort( a, first, first + length );
				continue;
			}
			
			final int shift = ( DIGITS_PER_ELEMENT - 1 - level % DIGITS_PER_ELEMENT ) * DIGIT_BITS; // This is the shift that extract the right byte from a key

			// Count keys.

			for( int i = length; i-- != 0; ) digit[ i ] = (byte)( ( ( KEY2LEXINT( a[ first + i ] ) >>> shift ) & DIGIT_MASK ) ^ signMask );
			for( int i = length; i-- != 0; ) count[ digit[ i ] & 0xFF ]++;
			// Compute cumulative distribution and push non-singleton keys on stack.
			int lastUsed = -1;
			
			for( int i = 0, p = 0; i < 1 << DIGIT_BITS; i++ ) {
				if ( count[ i ] != 0 ) {
					lastUsed = i;
					if ( level < maxLevel && count[ i ] > 1 ){
						//System.err.println( " Pushing " + new StackEntry( first + pos[ i - 1 ], first + pos[ i ], level + 1 ) );
						offsetStack[ offsetPos++ ] = p + first;
						lengthStack[ lengthPos++ ] = count[ i ];
						levelStack[ levelPos++ ] = level + 1;
					}
				}
				pos[ i ] = ( p += count[ i ] );
			}
			
			// When all slots are OK, the last slot is necessarily OK.
			final int end = length - count[ lastUsed ];
			count[ lastUsed ] = 0;

			// i moves through the start of each block
			for( int i = 0, c = -1, d; i < end; i += count[ c ], count[ c ] = 0 ) {
				KEY_TYPE t = a[ i + first ];
				c = digit[ i ] & 0xFF;
				while( ( d = --pos[ c ] ) > i ) {
					final KEY_TYPE z = t;
					final int zz = c;
					t = a[ d + first ];
					c = digit[ d ] & 0xFF;
					a[ d + first ] = z;
					digit[ d ] = (byte)zz;
				}

				a[ i + first ] = t;
			}
		}
	}



	private static KEY_GENERIC void insertionSortIndirect( final int[] perm, final KEY_TYPE[] a, final int from, final int to ) {
		for ( int i = from; ++i < to; ) { 
			int t = perm[ i ];
			int j = i;
			for ( int u = perm[ j - 1 ]; KEY_LESS( a[ t ], a[ u ] ); u = perm[ --j - 1 ] ) {
				perm[ j ] = u;
				if ( from == j - 1 ) {
					--j;
					break;
				}
			}
			perm[ j ] = t;
		}
	}

	/** Sorts the specified array using indirect radix sort.
	 * 
	 * <p>The sorting algorithm is a tuned radix sort adapted from Peter M. McIlroy, Keith Bostic and M. Douglas
	 * McIlroy, &ldquo;Engineering radix sort&rdquo;, <i>Computing Systems</i>, 6(1), pages 5&minus;27 (1993),
	 * and further improved using the digit-oracle idea described by
	 * Juha K&auml;rkk&auml;inen and Tommi Rantala in &ldquo;Engineering radix sort for strings&rdquo;,
	 * <i>String Processing and Information Retrieval, 15th International Symposium</i>, volume 5280 of
	 * Lecture Notes in Computer Science, pages 3&minus;14, Springer (2008).
	 *
	 * <p>This method implement an <em>indirect</em> sort. The elements of <code>perm</code> (which must
	 * be exactly the numbers in the interval <code>[0..perm.length)</code>) will be permuted so that
	 * <code>a[ perm[ i ] ] <= a[ perm[ i + 1 ] ]</code>.
	 *
	 * <p>This implementation is significantly faster than quicksort (unstable) or mergesort (stable)
	 * already at small sizes (say, more than 10000 elements), but it can only
	 * sort in ascending order. 
	 * It will allocate a support array of bytes with the same number of elements as the array to be sorted,
	 * and, in the stable case, a further support array as large as <code>perm</code> (note that the stable
	 * version is slightly faster).
	 * 
	 * @param perm a permutation array indexing <code>a</code>.
	 * @param a the array to be sorted.
	 * @param stable whether the sorting algorithm should be stable.
	 */
	public static void radixSortIndirect( final int[] perm, final KEY_TYPE[] a, final boolean stable ) {
		radixSortIndirect( perm, a, 0, perm.length, stable );
	}

	/** Sorts the specified array using indirect radix sort.
	 * 
	 * <p>The sorting algorithm is a tuned radix sort adapted from Peter M. McIlroy, Keith Bostic and M. Douglas
	 * McIlroy, &ldquo;Engineering radix sort&rdquo;, <i>Computing Systems</i>, 6(1), pages 5&minus;27 (1993),
	 * and further improved using the digit-oracle idea described by
	 * Juha K&auml;rkk&auml;inen and Tommi Rantala in &ldquo;Engineering radix sort for strings&rdquo;,
	 * <i>String Processing and Information Retrieval, 15th International Symposium</i>, volume 5280 of
	 * Lecture Notes in Computer Science, pages 3&minus;14, Springer (2008).
	 *
	 * <p>This method implement an <em>indirect</em> sort. The elements of <code>perm</code> (which must
	 * be exactly the numbers in the interval <code>[0..perm.length)</code>) will be permuted so that
	 * <code>a[ perm[ i ] ] <= a[ perm[ i + 1 ] ]</code>.
	 *
	 * <p>This implementation is significantly faster than quicksort (unstable) or mergesort (stable)
	 * already at small sizes (say, more than 10000 elements), but it can only
	 * sort in ascending order. 
	 * It will allocate a support array of bytes with the same number of elements as the array to be sorted,
	 * and, in the stable case, a further support array as large as <code>perm</code> (note that the stable
	 * version is slightly faster).
	 * 
	 * @param perm a permutation array indexing <code>a</code>.
	 * @param a the array to be sorted.
	 * @param from the index of the first element of <code>perm</code> (inclusive) to be permuted.
	 * @param to the index of the last element of <code>perm</code> (exclusive) to be permuted.
	 * @param stable whether the sorting algorithm should be stable.
	 */
	public static void radixSortIndirect( final int[] perm, final KEY_TYPE[] a, final int from, final int to, final boolean stable ) {
		final int maxLevel = DIGITS_PER_ELEMENT - 1;

		final int stackSize = ( ( 1 << DIGIT_BITS ) - 1 ) * ( DIGITS_PER_ELEMENT - 1 ) + 1;
		final int[] offsetStack = new int[ stackSize ];
		int offsetPos = 0;
		final int[] lengthStack = new int[ stackSize ];
		int lengthPos = 0;
		final int[] levelStack = new int[ stackSize ];
		int levelPos = 0;
		
		offsetStack[ offsetPos++ ] = from;
		lengthStack[ lengthPos++ ] = to - from;
		levelStack[ levelPos++ ] = 0;

		final int[] count = new int[ 1 << DIGIT_BITS ];
		final int[] pos = stable ? null : new int[ 1 << DIGIT_BITS ];
		final int[] support = stable ? new int[ perm.length ] : null;
		final byte[] digit = new byte[ to - from ];

		while( offsetPos > 0 ) {
			final int first = offsetStack[ --offsetPos ];
			final int length = lengthStack[ --lengthPos ];
			final int level = levelStack[ --levelPos ];
#if #keyclass(Character)
			final int signMask = 0;
#else
			final int signMask = level % DIGITS_PER_ELEMENT == 0 ? 1 << DIGIT_BITS - 1 : 0;
#endif
			
			if ( length < MEDIUM ) {
				insertionSortIndirect( perm, a, first, first + length );
				continue;
			}
			
			final int shift = ( DIGITS_PER_ELEMENT - 1 - level % DIGITS_PER_ELEMENT ) * DIGIT_BITS; // This is the shift that extract the right byte from a key

			// Count keys.
			for( int i = length; i-- != 0; ) digit[ i ] = (byte)( ( ( KEY2LEXINT( a[ perm[ first + i ] ] ) >>> shift ) & DIGIT_MASK ) ^ signMask );
			for( int i = length; i-- != 0; ) count[ digit[ i ] & 0xFF ]++;
			// Compute cumulative distribution and push non-singleton keys on stack.
			int lastUsed = -1;
			
			for( int i = 0, p = 0; i < 1 << DIGIT_BITS; i++ ) {
				if ( count[ i ] != 0 ) {
					lastUsed = i;
					if ( level < maxLevel && count[ i ] > 1 ){
						offsetStack[ offsetPos++ ] = p + first;
						lengthStack[ lengthPos++ ] = count[ i ];
						levelStack[ levelPos++ ] = level + 1;
					}
				}
				if ( stable ) count[ i ] = p += count[ i ];
				else pos[ i ] = ( p += count[ i ] );
			}
			
			if ( stable ) {
				for( int i = length; i-- != 0; ) support[ --count[ digit[ i ] & 0xFF ] ] = perm[ first + i ];
				System.arraycopy( support, 0, perm, first, length );
				it.unimi.dsi.fastutil.ints.IntArrays.fill( count, 0 );
			}
			else {
				// When all slots are OK, the last slot is necessarily OK.
				final int end = length - count[ lastUsed ];
				count[ lastUsed ] = 0;
				// i moves through the start of each block
				for( int i = 0, c = -1, d; i < end; i += count[ c ], count[ c ] = 0 ) {
					int t = perm[ i + first ];
					c = digit[ i ] & 0xFF;
					while( ( d = --pos[ c ] ) > i ) {
						final int z = t;
						final int zz = c;
						t = perm[ d + first ];
						c = digit[ d ] & 0xFF;
						perm[ d + first ] = z;
						digit[ d ] = (byte)zz;
					}

					perm[ i + first ] = t;
				}
			}
		}
	}



	private static void selectionSort( final KEY_TYPE[] a, final KEY_TYPE[] b, final int from, final int to ) {
		for( int i = from; i < to - 1; i++ ) {
			int m = i;
			for( int j = i + 1; j < to; j++ ) 
				if ( a[ j ] < a[ m ] || a[ j ] == a[ m ] && b[ j ] < b[ m ] ) m = j;
			
			if ( m != i ) {
				KEY_TYPE t = a[ i ];
				a[ i ] = a[ m ];
				a[ m ] = t;
				t = b[ i ];
				b[ i ] = b[ m ];
				b[ m ] = t;
			}
		}
	}

	/** Sorts the specified pair of arrays lexicographically using radix sort.
	 * <p>The sorting algorithm is a tuned radix sort adapted from Peter M. McIlroy, Keith Bostic and M. Douglas
	 * McIlroy, &ldquo;Engineering radix sort&rdquo;, <i>Computing Systems</i>, 6(1), pages 5&minus;27 (1993),
	 * and further improved using the digit-oracle idea described by
	 * Juha K&auml;rkk&auml;inen and Tommi Rantala in &ldquo;Engineering radix sort for strings&rdquo;,
	 * <i>String Processing and Information Retrieval, 15th International Symposium</i>, volume 5280 of
	 * Lecture Notes in Computer Science, pages 3&minus;14, Springer (2008).
	 *
	 * <p>This method implements a <em>lexicographical</em> sorting of the arguments. Pairs of elements
	 * in the same position in the two provided arrays will be considered a single key, and permuted
	 * accordingly. In the end, either <code>a[ i ] < a[ i + 1 ]</code> or <code>a[ i ] == a[ i + 1 ]</code> and <code>b[ i ] <= b[ i + 1 ]</code>.
	 *
	 * <p>This implementation is significantly faster than quicksort 
	 * already at small sizes (say, more than 10000 elements), but it can only
	 * sort in ascending order. It will allocate a support array of bytes with the same number of elements as the arrays to be sorted.
	 * 
	 * @param a the first array to be sorted.
	 * @param b the second array to be sorted.
	 */

	public static void radixSort( final KEY_TYPE[] a, final KEY_TYPE[] b ) {
		radixSort( a, b, 0, a.length );
	}
	
	/** Sorts the specified pair of arrays lexicographically using radix sort.
	 * 
	 * <p>The sorting algorithm is a tuned radix sort adapted from Peter M. McIlroy, Keith Bostic and M. Douglas
	 * McIlroy, &ldquo;Engineering radix sort&rdquo;, <i>Computing Systems</i>, 6(1), pages 5&minus;27 (1993),
	 * and further improved using the digit-oracle idea described by
	 * Juha K&auml;rkk&auml;inen and Tommi Rantala in &ldquo;Engineering radix sort for strings&rdquo;,
	 * <i>String Processing and Information Retrieval, 15th International Symposium</i>, volume 5280 of
	 * Lecture Notes in Computer Science, pages 3&minus;14, Springer (2008).
	 *
	 * <p>This method implements a <em>lexicographical</em> sorting of the arguments. Pairs of elements
	 * in the same position in the two provided arrays will be considered a single key, and permuted
	 * accordingly. In the end, either <code>a[ i ] < a[ i + 1 ]</code> or <code>a[ i ] == a[ i + 1 ]</code> and <code>b[ i ] <= b[ i + 1 ]</code>.
	 *
	 * <p>This implementation is significantly faster than quicksort 
	 * already at small sizes (say, more than 10000 elements), but it can only
	 * sort in ascending order. It will allocate a support array of bytes with the same number of elements as the arrays to be sorted.
	 * 
	 * @param a the first array to be sorted.
	 * @param b the second array to be sorted.
	 * @param from the index of the first element (inclusive) to be sorted.
	 * @param to the index of the last element (exclusive) to be sorted.
	 */
	public static void radixSort( final KEY_TYPE[] a, final KEY_TYPE[] b, final int from, final int to ) {
		final int layers = 2;
		if ( a.length != b.length ) throw new IllegalArgumentException( "Array size mismatch." );
		final int maxLevel = DIGITS_PER_ELEMENT * layers - 1;
		
		final int stackSize = ( ( 1 << DIGIT_BITS ) - 1 ) * ( layers * DIGITS_PER_ELEMENT - 1 ) + 1;
		final int[] offsetStack = new int[ stackSize ];
		int offsetPos = 0;
		final int[] lengthStack = new int[ stackSize ];
		int lengthPos = 0;
		final int[] levelStack = new int[ stackSize ];
		int levelPos = 0;
		
		offsetStack[ offsetPos++ ] = from;
		lengthStack[ lengthPos++ ] = to - from;
		levelStack[ levelPos++ ] = 0;

		final int[] count = new int[ 1 << DIGIT_BITS ];
		final int[] pos = new int[ 1 << DIGIT_BITS ];
		final byte[] digit = new byte[ to - from ];

		while( offsetPos > 0 ) {
			final int first = offsetStack[ --offsetPos ];
			final int length = lengthStack[ --lengthPos ];
			final int level = levelStack[ --levelPos ];
#if #keyclass(Character)
			final int signMask = 0;
#else
			final int signMask = level % DIGITS_PER_ELEMENT == 0 ? 1 << DIGIT_BITS - 1 : 0;
#endif
			
			if ( length < MEDIUM ) {
				selectionSort( a, b, first, first + length );
				continue;
			}
			
			final KEY_TYPE[] k = level < DIGITS_PER_ELEMENT ? a : b; // This is the key array
			final int shift = ( DIGITS_PER_ELEMENT - 1 - level % DIGITS_PER_ELEMENT ) * DIGIT_BITS; // This is the shift that extract the right byte from a key

			// Count keys.
			for( int i = length; i-- != 0; ) digit[ i ] = (byte)( ( ( KEY2LEXINT( k[ first + i ] ) >>> shift ) & DIGIT_MASK ) ^ signMask );
			for( int i = length; i-- != 0; ) count[ digit[ i ] & 0xFF ]++;
			// Compute cumulative distribution and push non-singleton keys on stack.
			int lastUsed = -1;

			for( int i = 0, p = 0; i < 1 << DIGIT_BITS; i++ ) {
				if ( count[ i ] != 0 ) {
					lastUsed = i;
					if ( level < maxLevel && count[ i ] > 1 ){
						offsetStack[ offsetPos++ ] = p + first;
						lengthStack[ lengthPos++ ] = count[ i ];
						levelStack[ levelPos++ ] = level + 1;
					}
				}
				pos[ i ] = ( p += count[ i ] );
			}

			// When all slots are OK, the last slot is necessarily OK.
			final int end = length - count[ lastUsed ];
			count[ lastUsed ] = 0;
			
			// i moves through the start of each block
			for( int i = 0, c = -1, d; i < end; i += count[ c ], count[ c ] = 0 ) {
				KEY_TYPE t = a[ i + first ];
				KEY_TYPE u = b[ i + first ];
				c = digit[ i ] & 0xFF;
				while( ( d = --pos[ c ] ) > i ) {
					KEY_TYPE z = t;
					final int zz = c;
					t = a[ d + first ];
					a[ d + first ] = z;
					z = u;
					u = b[ d + first ];
					b[ d + first ] = z;
					c = digit[ d ] & 0xFF;
					digit[ d ] = (byte)zz;
				}

				a[ i + first ] = t;
				b[ i + first ] = u;
			}
		}
	}




	private static KEY_GENERIC void insertionSortIndirect( final int[] perm, final KEY_TYPE[] a, final KEY_TYPE[] b, final int from, final int to ) {
		for ( int i = from; ++i < to; ) { 
			int t = perm[ i ];
			int j = i;
			for ( int u = perm[ j - 1 ]; KEY_LESS( a[ t ], a[ u ] ) || KEY_CMP_EQ( a[ t ], a[ u ] ) && KEY_LESS( b[ t ], b[ u ] ); u = perm[ --j - 1 ] ) {
				perm[ j ] = u;
				if ( from == j - 1 ) {
					--j;
					break;
				}
			}
			perm[ j ] = t;
		}
	}

	/** Sorts the specified pair of arrays lexicographically using indirect radix sort.
	 * 
	 * <p>The sorting algorithm is a tuned radix sort adapted from Peter M. McIlroy, Keith Bostic and M. Douglas
	 * McIlroy, &ldquo;Engineering radix sort&rdquo;, <i>Computing Systems</i>, 6(1), pages 5&minus;27 (1993),
	 * and further improved using the digit-oracle idea described by
	 * Juha K&auml;rkk&auml;inen and Tommi Rantala in &ldquo;Engineering radix sort for strings&rdquo;,
	 * <i>String Processing and Information Retrieval, 15th International Symposium</i>, volume 5280 of
	 * Lecture Notes in Computer Science, pages 3&minus;14, Springer (2008).
	 *
	 * <p>This method implement an <em>indirect</em> sort. The elements of <code>perm</code> (which must
	 * be exactly the numbers in the interval <code>[0..perm.length)</code>) will be permuted so that
	 * <code>a[ perm[ i ] ] <= a[ perm[ i + 1 ] ]</code>.
	 *
	 * <p>This implementation is significantly faster than quicksort (unstable) or mergesort (stable)
	 * already at small sizes (say, more than 10000 elements), but it can only
	 * sort in ascending order. 
	 * It will allocate a support array of bytes with the same number of elements as the array to be sorted,
	 * and, in the stable case, a further support array as large as <code>perm</code> (note that the stable
	 * version is slightly faster).
	 * 
	 * @param perm a permutation array indexing <code>a</code>.
	 * @param a the array to be sorted.
	 * @param b the second array to be sorted.
	 * @param stable whether the sorting algorithm should be stable.
	 */
	public static void radixSortIndirect( final int[] perm, final KEY_TYPE[] a, final KEY_TYPE[] b, final boolean stable ) {
		radixSortIndirect( perm, a, b, 0, perm.length, stable );
	}

	/** Sorts the specified pair of arrays lexicographically using indirect radix sort.
	 * 
	 * <p>The sorting algorithm is a tuned radix sort adapted from Peter M. McIlroy, Keith Bostic and M. Douglas
	 * McIlroy, &ldquo;Engineering radix sort&rdquo;, <i>Computing Systems</i>, 6(1), pages 5&minus;27 (1993),
	 * and further improved using the digit-oracle idea described by
	 * Juha K&auml;rkk&auml;inen and Tommi Rantala in &ldquo;Engineering radix sort for strings&rdquo;,
	 * <i>String Processing and Information Retrieval, 15th International Symposium</i>, volume 5280 of
	 * Lecture Notes in Computer Science, pages 3&minus;14, Springer (2008).
	 *
	 * <p>This method implement an <em>indirect</em> sort. The elements of <code>perm</code> (which must
	 * be exactly the numbers in the interval <code>[0..perm.length)</code>) will be permuted so that
	 * <code>a[ perm[ i ] ] <= a[ perm[ i + 1 ] ]</code>.
	 *
	 * <p>This implementation is significantly faster than quicksort (unstable) or mergesort (stable)
	 * already at small sizes (say, more than 10000 elements), but it can only
	 * sort in ascending order. 
	 * It will allocate a support array of bytes with the same number of elements as the array to be sorted,
	 * and, in the stable case, a further support array as large as <code>perm</code> (note that the stable
	 * version is slightly faster).
	 * 
	 * @param perm a permutation array indexing <code>a</code>.
	 * @param a the array to be sorted.
	 * @param b the second array to be sorted.
	 * @param from the index of the first element of <code>perm</code> (inclusive) to be permuted.
	 * @param to the index of the last element of <code>perm</code> (exclusive) to be permuted.
	 * @param stable whether the sorting algorithm should be stable.
	 */
	public static void radixSortIndirect( final int[] perm, final KEY_TYPE[] a, final KEY_TYPE[] b, final int from, final int to, final boolean stable ) {
		final int layers = 2;
		if ( a.length != b.length ) throw new IllegalArgumentException( "Array size mismatch." );
		final int maxLevel = DIGITS_PER_ELEMENT * layers - 1;
		
		final int stackSize = ( ( 1 << DIGIT_BITS ) - 1 ) * ( layers * DIGITS_PER_ELEMENT - 1 ) + 1;
		final int[] offsetStack = new int[ stackSize ];
		int offsetPos = 0;
		final int[] lengthStack = new int[ stackSize ];
		int lengthPos = 0;
		final int[] levelStack = new int[ stackSize ];
		int levelPos = 0;
		
		offsetStack[ offsetPos++ ] = from;
		lengthStack[ lengthPos++ ] = to - from;
		levelStack[ levelPos++ ] = 0;

		final int[] count = new int[ 1 << DIGIT_BITS ];
		final int[] pos = stable ? null : new int[ 1 << DIGIT_BITS ];
		final int[] support = stable ? new int[ perm.length ] : null;
		final byte[] digit = new byte[ to - from ];

		while( offsetPos > 0 ) {
			final int first = offsetStack[ --offsetPos ];
			final int length = lengthStack[ --lengthPos ];
			final int level = levelStack[ --levelPos ];
#if #keyclass(Character)
			final int signMask = 0;
#else
			final int signMask = level % DIGITS_PER_ELEMENT == 0 ? 1 << DIGIT_BITS - 1 : 0;
#endif
			
			if ( length < MEDIUM ) {
				insertionSortIndirect( perm, a, b, first, first + length );
				continue;
			}
			
			final KEY_TYPE[] k = level < DIGITS_PER_ELEMENT ? a : b; // This is the key array
			final int shift = ( DIGITS_PER_ELEMENT - 1 - level % DIGITS_PER_ELEMENT ) * DIGIT_BITS; // This is the shift that extract the right byte from a key

			// Count keys.
			for( int i = length; i-- != 0; ) digit[ i ] = (byte)( ( ( KEY2LEXINT( k[ perm[ first + i ] ] ) >>> shift ) & DIGIT_MASK ) ^ signMask );
			for( int i = length; i-- != 0; ) count[ digit[ i ] & 0xFF ]++;
			// Compute cumulative distribution and push non-singleton keys on stack.
			int lastUsed = -1;
			
			for( int i = 0, p = 0; i < 1 << DIGIT_BITS; i++ ) {
				if ( count[ i ] != 0 ) {
					lastUsed = i;
					if ( level < maxLevel && count[ i ] > 1 ){
						offsetStack[ offsetPos++ ] = p + first;
						lengthStack[ lengthPos++ ] = count[ i ];
						levelStack[ levelPos++ ] = level + 1;
					}
				}
				if ( stable ) count[ i ] = p += count[ i ];
				else pos[ i ] = ( p += count[ i ] );
			}
			
			if ( stable ) {
				for( int i = length; i-- != 0; ) support[ --count[ digit[ i ] & 0xFF ] ] = perm[ first + i ];
				System.arraycopy( support, 0, perm, first, length );
				it.unimi.dsi.fastutil.ints.IntArrays.fill( count, 0 );
			}
			else {
				// When all slots are OK, the last slot is necessarily OK.
				final int end = length - count[ lastUsed ];
				count[ lastUsed ] = 0;
				// i moves through the start of each block
				for( int i = 0, c = -1, d; i < end; i += count[ c ], count[ c ] = 0 ) {
					int t = perm[ i + first ];
					c = digit[ i ] & 0xFF;
					while( ( d = --pos[ c ] ) > i ) {
						final int z = t;
						final int zz = c;
						t = perm[ d + first ];
						c = digit[ d ] & 0xFF;
						perm[ d + first ] = z;
						digit[ d ] = (byte)zz;
					}

					perm[ i + first ] = t;
				}
			}
		}
	}




	private static void selectionSort( final KEY_TYPE[][] a, final int from, final int to, final int level ) {
		final int layers = a.length;
		final int firstLayer = level / DIGITS_PER_ELEMENT;

		for( int i = from; i < to - 1; i++ ) {
			int m = i;
			for( int j = i + 1; j < to; j++ ) {
				for( int p = firstLayer; p < layers; p++ ) {
					if ( a[ p ][ j ] < a[ p ][ m ] ) {
						m = j;
						break;
					}
					else if ( a[ p ][ j ] > a[ p ][ m ] ) break;
				}
			}
			if ( m != i ) {
				for( int p = layers; p-- != 0; ) {
					final KEY_TYPE u = a[ p ][ i ];
					a[ p ][ i ] = a[ p ][ m ];
					a[ p ][ m ] = u;
				}
			}
		}
	}


	
	/** Sorts the specified array of arrays lexicographically using radix sort.
	 * 
	 * <p>The sorting algorithm is a tuned radix sort adapted from Peter M. McIlroy, Keith Bostic and M. Douglas
	 * McIlroy, &ldquo;Engineering radix sort&rdquo;, <i>Computing Systems</i>, 6(1), pages 5&minus;27 (1993),
	 * and further improved using the digit-oracle idea described by
	 * Juha K&auml;rkk&auml;inen and Tommi Rantala in &ldquo;Engineering radix sort for strings&rdquo;,
	 * <i>String Processing and Information Retrieval, 15th International Symposium</i>, volume 5280 of
	 * Lecture Notes in Computer Science, pages 3&minus;14, Springer (2008).
	 *
	 * <p>This method implements a <em>lexicographical</em> sorting of the provided arrays. Tuples of elements
	 * in the same position will be considered a single key, and permuted
	 * accordingly.
	 *
	 * <p>This implementation is significantly faster than quicksort 
	 * already at small sizes (say, more than 10000 elements), but it can only
	 * sort in ascending order. It will allocate a support array of bytes with the same number of elements as the arrays to be sorted.
	 * 
	 * @param a an array containing arrays of equal length to be sorted lexicographically in parallel.
	 */
	public static void radixSort( final KEY_TYPE[][] a ) {
		radixSort( a, 0, a[ 0 ].length );
	}

	/** Sorts the specified array of arrays lexicographically using radix sort.
	 * 
	 * <p>The sorting algorithm is a tuned radix sort adapted from Peter M. McIlroy, Keith Bostic and M. Douglas
	 * McIlroy, &ldquo;Engineering radix sort&rdquo;, <i>Computing Systems</i>, 6(1), pages 5&minus;27 (1993),
	 * and further improved using the digit-oracle idea described by
	 * Juha K&auml;rkk&auml;inen and Tommi Rantala in &ldquo;Engineering radix sort for strings&rdquo;,
	 * <i>String Processing and Information Retrieval, 15th International Symposium</i>, volume 5280 of
	 * Lecture Notes in Computer Science, pages 3&minus;14, Springer (2008).
	 *
	 * <p>This method implements a <em>lexicographical</em> sorting of the provided arrays. Tuples of elements
	 * in the same position will be considered a single key, and permuted
	 * accordingly.
	 *
	 * <p>This implementation is significantly faster than quicksort 
	 * already at small sizes (say, more than 10000 elements), but it can only
	 * sort in ascending order. It will allocate a support array of bytes with the same number of elements as the arrays to be sorted.
	 * 
	 * @param a an array containing arrays of equal length to be sorted lexicographically in parallel.
	 * @param from the index of the first element (inclusive) to be sorted.
	 * @param to the index of the last element (exclusive) to be sorted.
	 */
	public static void radixSort( final KEY_TYPE[][] a, final int from, final int to ) {
		final int layers = a.length;
		final int maxLevel = DIGITS_PER_ELEMENT * layers - 1;
		for( int p = layers, l = a[ 0 ].length; p-- != 0; ) if ( a[ p ].length != l ) throw new IllegalArgumentException( "The array of index " + p + " has not the same length of the array of index 0." );

		final int stackSize = ( ( 1 << DIGIT_BITS ) - 1 ) * ( layers * DIGITS_PER_ELEMENT - 1 ) + 1;
		final int[] offsetStack = new int[ stackSize ];
		int offsetPos = 0;
		final int[] lengthStack = new int[ stackSize ];
		int lengthPos = 0;
		final int[] levelStack = new int[ stackSize ];
		int levelPos = 0;
		
		offsetStack[ offsetPos++ ] = from;
		lengthStack[ lengthPos++ ] = to - from;
		levelStack[ levelPos++ ] = 0;

		final int[] count = new int[ 1 << DIGIT_BITS ];
		final int[] pos = new int[ 1 << DIGIT_BITS ];
		final byte[] digit = new byte[ to - from ];
		final KEY_TYPE[] t = new KEY_TYPE[ layers ];

		while( offsetPos > 0 ) {
			final int first = offsetStack[ --offsetPos ];
			final int length = lengthStack[ --lengthPos ];
			final int level = levelStack[ --levelPos ];
#if #keyclass(Character)
			final int signMask = 0;
#else
			final int signMask = level % DIGITS_PER_ELEMENT == 0 ? 1 << DIGIT_BITS - 1 : 0;
#endif
			
			if ( length < MEDIUM ) {
				selectionSort( a, first, first + length, level );
				continue;
			}
			
			final KEY_TYPE[] k = a[ level / DIGITS_PER_ELEMENT ]; // This is the key array
			final int shift = ( DIGITS_PER_ELEMENT - 1 - level % DIGITS_PER_ELEMENT ) * DIGIT_BITS; // This is the shift that extract the right byte from a key

			// Count keys.
			for( int i = length; i-- != 0; ) digit[ i ] = (byte)( ( KEY2LEXINT( k[ first + i ] ) >>> shift & DIGIT_MASK ) ^ signMask );
			for( int i = length; i-- != 0; ) count[ digit[ i ] & 0xFF ]++;
			// Compute cumulative distribution and push non-singleton keys on stack.
			int lastUsed = -1;
			
			for( int i = 0, p = 0; i < 1 << DIGIT_BITS; i++ ) {
				if ( count[ i ] != 0 ) {
					lastUsed = i;
					if ( level < maxLevel && count[ i ] > 1 ){
						offsetStack[ offsetPos++ ] = p + first;
						lengthStack[ lengthPos++ ] = count[ i ];
						levelStack[ levelPos++ ] = level + 1;
					}
				}
				pos[ i ] = ( p += count[ i ] );
			}

			// When all slots are OK, the last slot is necessarily OK.
			final int end = length - count[ lastUsed ];
			count[ lastUsed ] = 0;

			// i moves through the start of each block
			for( int i = 0, c = -1, d; i < end; i += count[ c ], count[ c ] = 0 ) {
				for( int p = layers; p-- != 0; ) t[ p ] = a[ p ][ i + first ];
				c = digit[ i ] & 0xFF;
				
				 while( ( d = --pos[ c ] ) > i ) {
					for( int p = layers; p-- != 0; ) {
						final KEY_TYPE u = t[ p ];
						t[ p ] = a[ p ][ d + first ];
						a[ p ][ d + first ] = u;
					}
					final int zz = c;
					c = digit[ d ] & 0xFF;
					digit[ d ] = (byte)zz;
				}

				for( int p = layers; p-- != 0; ) a[ p ][ i + first ] = t[ p ];
			}
		}
	}


#endif

#endif

	/** Shuffles the specified array fragment using the specified pseudorandom number generator.
	 * 
	 * @param a the array to be shuffled.
	 * @param from the index of the first element (inclusive) to be shuffled.
	 * @param to the index of the last element (exclusive) to be shuffled.
	 * @param random a pseudorandom number generator (please use a <a href="http://dsiutils.dsi.unimi.it/docs/it/unimi/dsi/util/XorShiftStarRandom.html">XorShift*</a> generator).
	 * @return <code>a</code>.
	 */
	public static KEY_GENERIC KEY_GENERIC_TYPE[] shuffle( final KEY_GENERIC_TYPE[] a, final int from, final int to, final Random random ) {
		for( int i = to - from; i-- != 0; ) {
			final int p = random.nextInt( i + 1 ); 
			final KEY_GENERIC_TYPE t = a[ from + i ];
			a[ from + i ] = a[ from + p ];
			a[ from + p ] = t;
		}
		return a;
	}

	/** Shuffles the specified array using the specified pseudorandom number generator.
	 * 
	 * @param a the array to be shuffled.
	 * @param random a pseudorandom number generator (please use a <a href="http://dsiutils.dsi.unimi.it/docs/it/unimi/dsi/util/XorShiftStarRandom.html">XorShift*</a> generator).
	 * @return <code>a</code>.
	 */
	public static KEY_GENERIC KEY_GENERIC_TYPE[] shuffle( final KEY_GENERIC_TYPE[] a, final Random random ) {
		for( int i = a.length; i-- != 0; ) {
			final int p = random.nextInt( i + 1 ); 
			final KEY_GENERIC_TYPE t = a[ i ];
			a[ i ] = a[ p ];
			a[ p ] = t;
		}
		return a;
	}

	/** Reverses the order of the elements in the specified array.
	 * 
	 * @param a the array to be reversed.
	 * @return <code>a</code>.
	 */
	public static KEY_GENERIC KEY_GENERIC_TYPE[] reverse( final KEY_GENERIC_TYPE[] a ) {
		final int length = a.length;
		for( int i = length / 2; i-- != 0; ) {
			final KEY_GENERIC_TYPE t = a[ length - i - 1 ];
			a[ length - i - 1 ] = a[ i ];
			a[ i ] = t;
		}
		return a;
	}

	/** Reverses the order of the elements in the specified array fragment.
	 * 
	 * @param a the array to be reversed.
	 * @param from the index of the first element (inclusive) to be reversed.
	 * @param to the index of the last element (exclusive) to be reversed.
	 * @return <code>a</code>.
	 */
	public static KEY_GENERIC KEY_GENERIC_TYPE[] reverse( final KEY_GENERIC_TYPE[] a, final int from, final int to ) {
		final int length = to - from;
		for( int i = length / 2; i-- != 0; ) {
			final KEY_GENERIC_TYPE t = a[ from + length - i - 1 ];
			a[ from + length - i - 1 ] = a[ from + i ];
			a[ from + i ] = t;
		}
		return a;
	}

	/** A type-specific content-based hash strategy for arrays. */

	private static final class ArrayHashStrategy KEY_GENERIC implements Hash.Strategy<KEY_GENERIC_TYPE[]>, java.io.Serializable {
		private static final long serialVersionUID = -7046029254386353129L;

		public int hashCode( final KEY_GENERIC_TYPE[] o ) {
			return java.util.Arrays.hashCode( o );
		}
		
		public boolean equals( final KEY_GENERIC_TYPE[] a, final KEY_GENERIC_TYPE[] b ) {
			return java.util.Arrays.equals( a, b );
		}
	}

	/** A type-specific content-based hash strategy for arrays.
	 *
	 * <P>This hash strategy may be used in custom hash collections whenever keys are
	 * arrays, and they must be considered equal by content. This strategy
	 * will handle <code>null</code> correctly, and it is serializable.
	 */

#if #keys(primitive)
	public final static Hash.Strategy<KEY_TYPE[]> HASH_STRATEGY = new ArrayHashStrategy();
#else
	@SuppressWarnings({"rawtypes"})
	public final static Hash.Strategy HASH_STRATEGY = new ArrayHashStrategy();
#endif

}