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SUBROUTINE ETRBMD
C
C BASIC BENDING TRIANGLE ELEMENT ROUTINE
C DOUBLE PRECISION VERSION
C
C THIS SUBROUTINE CALCULATES THE COUPLED MASS MATRIX FOR THE BASIC
C BENDING TRIANGLE.
C
C ECPT LIST FOR BASIC BENDING TRIANGLE NAME IN
C THIS
C ECPT ROUTINE TYPE
C ******************************************************************
C ECPT( 1) = ELEMENT ID NECPT(1) INTEGER
C ECPT( 2) = GRID POINT A NGRID(1) INTEGER
C ECPT( 3) = GRID POINT B NGRID(2) INTEGER
C ECPT( 4) = GRID POINT C NGRID(3) INTEGER
C ECPT( 5) = THETA = ANGLE OF MATERIAL ANGLE REAL
C ECPT( 6) = MATERIAL ID 1 MATID1 INTEGER
C ECPT( 7) = I = MOMENT OF INERTIA EYE REAL
C ECPT( 8) = MATERIAL ID 2 MATID2 INTEGER
C ECPT( 9) = T2 T2 REAL
C ECPT(10) = NON-STRUCTURAL-MASS FMU REAL
C ECPT(11) = Z1 Z11 REAL
C ECPT(12) = Z2 Z22 REAL
C ECPT(13) = COORD. SYSTEM ID 1 NECPT(13) INTEGER
C ECPT(14) = X1 X1 REAL
C ECPT(15) = Y1 Y1 REAL
C ECPT(16) = Z1 Z1 REAL
C ECPT(17) = COORD. SYSTEM ID 2 NECPT(17) INTEGER
C ECPT(18) = X2 X2 REAL
C ECPT(19) = Y2 Y2 REAL
C ECPT(20) = Z2 Z2 REAL
C ECPT(21) = COORD. SYSTEM ID 3 NECPT(21) INTEGER
C ECPT(22) = X3 X3 REAL
C ECPT(23) = Y3 Y3 REAL
C ECPT(24) = Z3 Z3 REAL
C ECPT(25) = ELEMENT TEMPERATURE ELTEMP REAL
C
LOGICAL NOGO
INTEGER NECPT(26)
REAL ECPT(26)
DOUBLE PRECISION D(9),G(9),G2X2(4),J2X2(4),S(18),HYQ(6),SIIJ(7,7),
1 MBARAA(9),MAR(18),MRR(36),A,PROD9,TEMP9,XSUBB,
2 XSUBC,YSUBC,BFACT,E,AOUT,DETERM,TEMP,XCSQ,YCSQ,
3 XBSQ,XCYC,YPRODJ,FJ,FJ2,AIJ,BIJ,XPRODI,FI,FIJ,
4 SIZERO
COMMON /EMGPRM/ DUM(15),ISMB(3),IPREC,NOGO
COMMON /MATIN / MATID,INFLAG,ELTEMP,STRESS,SINTH,COSTH
COMMON /MATOUT/ G11,G12,G13,G22,G23,G33,RHO,ALPHA1,ALPHA2,ALP12,
1 T SUB 0,G SUB E,SIGTEN,SIGCOM,SIGSHE,
2 G2X211,G2X212,G2X222,SPACE(2)
COMMON /EMGEST/ IELID,NGRID(3),ANGLE,MATID1,EYE,MATID2,T2,FMU,
1 Z11,Z22,DUMMY1,X1,Y1,Z1,DUMMY2,X2,Y2,Z2,DUMMY3,
2 X3,Y3,Z3,DUMB(76)
COMMON /EMGTRX/ A(225),PROD9(9),TEMP9(9),XSUBB,XSUBC,YSUBC,
1 BFACT,E(18),AOUT(324)
EQUIVALENCE (IELID,ECPT(1),NECPT(1)),(J2X2(1),A(14)),
1 (D(1),G(1),A(1),SIIJ(1,1)),(G2X2(1),A(10)),
2 (HYQ(1),A(50)),(MBARAA(1),A(136)),
3 (MAR(1),A(145)),(MRR(1),A(163)),(S(1),A(82))
C
C SETTING UP G MATRIX
C BEFORE THIS SUBROUTINE CAN FUNCTION SEVERAL TERMS MUST BE DEFINED
C SEE ETRBKD.
C
C POSSIBLE ERROR SOURCE FIX. MAY REQUIRE LOADER CHANGE.
C IF (ISMB(1) .EQ. 0) CALL ETRBKD (1)
C
INFLAG = 2
MATID = MATID1
CALL MAT (ECPT(1))
C
C FILL G-MATRIX WITH OUTPUT FROM MAT ROUTINE
C
G(1) = G11
G(2) = G12
G(3) = G13
G(4) = G12
G(5) = G22
G(6) = G23
G(7) = G13
G(8) = G23
G(9) = G33
C
DO 350 I = 1,9
350 D(I) = G(I)*DBLE(EYE)
C
C F1LL (HBAR) MATRIX STORING AT A(100). . .A(135)
C
XCSQ = XSUBC**2
YCSQ = YSUBC**2
XBSQ = XSUBB**2
XCYC = XSUBC*YSUBC
C
DO 380 I = 100,135
380 A(I) = 0.
C
A(100) = XBSQ
A(103) = XBSQ*XSUBB
A(107) = XSUBB
A(112) =-2.*XSUBB
A(115) =-3.*XBSQ
A(118) = XCSQ
A(119) = XCYC
A(120) = YCSQ
A(121) = XCSQ*XSUBC
A(122) = YCSQ*XSUBC
A(123) = YCSQ*YSUBC
A(125) = XSUBC
A(126) = YSUBC*2.0D0
A(128) = XCYC *2.0D0
A(129) = YCSQ *3.0D0
A(130) =-2.0D0*XSUBC
A(131) =-YSUBC
A(133) =-3.0D0*XCSQ
A(134) =-YCSQ
C
IF (T2 .EQ. 0.) GO TO 410
C
C ALL OF THE FOLLOWING OPERATIONS THROUGH STATEMENT LABEL 110
C ARE NECESSARY IF T2 IS NON-ZERO.
C
C GET THE G2X2 MATRIX
C
MATID = MATID2
INFLAG = 3
CALL MAT (ECPT(1))
IF (G2X211.EQ.0.0 .AND. G2X212.EQ.0.0 .AND. G2X222.EQ.0.0)
1 GO TO 410
C
G2X2(1) = DBLE(G2X211)*DBLE(T2)
G2X2(2) = DBLE(G2X212)*DBLE(T2)
G2X2(4) = DBLE(G2X222)*DBLE(T2)
C
DETERM = G2X2(1)*G2X2(4) - G2X2(3)*G2X2(2)
J2X2(1) = G2X2(4)/DETERM
J2X2(2) =-G2X2(2)/DETERM
J2X2(3) = J2X2(2)
J2X2(4) = G2X2(1)/DETERM
C
C (H ) IS PARTITIONED INTO A LEFT AND RIGHT PORTION AND ONLY THE
C YQ RIGHT PORTION IS COMPUTED AND USED AS A (2X3). THE LEFT
C 2X3 PORTION IS NULL. THE RIGHT PORTION WILL BE STORED AT
C A(50)...A(55) UNTIL NOT NEEDED ANY FURTHER.
C
TEMP = 2.*D(2) + 4.*D(9)
HYQ(1) = -6.*(J2X2(1)*D(1) + J2X2(2)*D(3))
HYQ(2) = -J2X2(1)*TEMP - 6.*J2X2(2)*D(6)
HYQ(3) = -6.*(J2X2(1)*D(6) + J2X2(2)*D(5))
HYQ(4) = -6.*(J2X2(2)*D(1) + J2X2(4)*D(3))
HYQ(5) = -J2X2(2)*TEMP - 6.*J2X2(4)*D(6)
HYQ(6) = -6.*(J2X2(2)*D(6) + J2X2(4)*D(5))
C
C ADD TO 6 OF THE (HBAR) ELEMENTS THE RESULT OF (H )(H )
C UY YQ
C THE PRODUCT IS FORMED DIRECTLY IN THE ADDITION PROCESS BELOW.
C NO (H ) MATRIX IS ACTUALLY COMPUTED DIRECTLY.
C UY
C
C THE FOLLOWING IS THEN STEP 6 PAGE 8, FMMS-66
C
DO 400 I = 1,3
A(I+102) = A(I+102) + XSUBB*HYQ(I)
400 A(I+120) = A(I+120) + XSUBC*HYQ(I) + YSUBC*HYQ(I+3)
C
C THIS ENDS ADDED COMPUTATION FOR CASE OF T2 NOT ZERO
C
410 CONTINUE
C
C AT THIS POINT INVERT (H) WHICH IS STORED AT A(100). . .A(135)
C STORE INVERSE BACK IN A(100). . A(135)
C NO NEED TO COMPUTE DETERMINANT SINCE IT IS NOT USED SUBSEQUENTLY.
C
ISING = -1
CALL INVERD (6,A(100),6, A(136),0,DETERM,ISING,A(142))
C
C CHECK TO SEE IF H WAS SINGULAR
C
IF (ISING .EQ. 2) GO TO 600
C
C ISING = 2 IMPLIES SINGULAR MATRIX THUS ERROR CONDITION.
C
C CHUNK OUT INTEGRAL VALUES I USED IN REFERENCED M MATRICES
C IJ SEE P.9, FMMS-66
C
C THE CALCULATION FOR (I ) ARE AS FOLLOWS
C IJ
C ***
C A1 = XSUBB * YSUBC**(J+1) / ((J+1)*(J+2)) *
C 0J *
C *
C B = XSUBC * YSUBC**(J+1) / (J+2) *
C 0J ** J=0,6
C *
C A = A1 + B *
C 0J 0J 0J *
C *
C I = MU * A1 *
C 0J 0J ***
C
C ***
C A1 = I * XSUBB * A /(I+J+2) *
C IJ I-1,J *
C *
C B = XSUBC**(I+1) * YSUBC**(J+1) /((I+1)*(I+J+2)) * I=1,6
C IJ ** J=0,6
C *
C A = A1 + B *
C IJ IJ IJ *
C *
C I MU * A1 *
C IJ= IJ *
C ***
C NOTE.. LOOPS FOR PROGRAM BEGIN AT 1 INSTEAD OF 0
C I.E. I = 1,7
C J = 1,7
C
DO 440 J = 1,7
YPRODJ = YSUBC**J
FJ = J
FJ2 = J + 1
AIJ = XSUBB*YPRODJ/(FJ*FJ2)
BIJ = XSUBC*YPRODJ/FJ2
SIIJ(1,J) = FMU*AIJ
AIJ = AIJ + BIJ
IF (J .EQ. 7) GO TO 440
K = 8 - J
DO 430 I = 2,K
XPRODI = XSUBC**I
FI = I
FIJ = I + J
AIJ = (FI-1.)*XSUBB*AIJ/FIJ
BIJ = XPRODI*YPRODJ/(FI*FIJ)
SIIJ(I,J) = FMU*AIJ
430 AIJ = AIJ + BIJ
C
440 CONTINUE
SIZERO = SIIJ(1,1)/3.
C
C CHUNK IN NUMBERS FOR (M-BAR-AA) 3X3 MATRIX AS PER MS-48, PP. 6-10
C
C (M ) 3X6 MATRIX
C AR
C
C (M ) 6X6 MATRIX
C RR
C
C (M-BAR-AA) MATRIX
C
MBARAA(1) = SIIJ(1,1)
MBARAA(2) = SIIJ(1,2)
MBARAA(3) = -SIIJ(2,1)
MBARAA(4) = SIIJ(1,2)
MBARAA(5) = SIIJ(1,3)
MBARAA(6) = -SIIJ(2,2)
MBARAA(7) = -SIIJ(2,1)
MBARAA(8) = -SIIJ(2,2)
MBARAA(9) = SIIJ(3,1)
C
C (M ) MATRIX
C AR
C
MAR( 1) = SIIJ(3,1)
MAR( 2) = SIIJ(2,2)
MAR( 3) = SIIJ(1,3)
MAR( 4) = SIIJ(4,1)
MAR( 5) = SIIJ(2,3)
MAR( 6) = SIIJ(1,4)
MAR( 7) = SIIJ(3,2)
MAR( 8) = SIIJ(2,3)
MAR( 9) = SIIJ(1,4)
MAR(10) = SIIJ(4,2)
MAR(11) = SIIJ(2,4)
MAR(12) = SIIJ(1,5)
MAR(13) =-SIIJ(4,1)
MAR(14) =-SIIJ(3,2)
MAR(15) =-SIIJ(2,3)
MAR(16) =-SIIJ(5,1)
MAR(17) =-SIIJ(3,3)
MAR(18) =-SIIJ(2,4)
C
C (M ) MATRIX A 6X6 SYMMETRIC MATRIX
C RR
C
MRR( 1) = SIIJ(5,1)
MRR( 2) = SIIJ(4,2)
MRR( 3) = SIIJ(3,3)
MRR( 4) = SIIJ(6,1)
MRR( 5) = SIIJ(4,3)
MRR( 6) = SIIJ(3,4)
MRR( 7) = MRR(2)
MRR( 8) = SIIJ(3,3)
MRR( 9) = SIIJ(2,4)
MRR(10) = SIIJ(5,2)
MRR(11) = SIIJ(3,4)
MRR(12) = SIIJ(2,5)
MRR(13) = MRR(3)
MRR(14) = MRR(9)
MRR(15) = SIIJ(1,5)
MRR(16) = SIIJ(4,3)
MRR(17) = SIIJ(2,5)
MRR(18) = SIIJ(1,6)
MRR(19) = MRR( 4)
MRR(20) = MRR(10)
MRR(21) = MRR(16)
MRR(22) = SIIJ(7,1)
MRR(23) = SIIJ(5,3)
MRR(24) = SIIJ(4,4)
MRR(25) = MRR( 5)
MRR(26) = MRR(11)
MRR(27) = MRR(17)
MRR(28) = MRR(23)
MRR(29) = SIIJ(3,5)
MRR(30) = SIIJ(2,6)
MRR(31) = MRR( 6)
MRR(32) = MRR(12)
MRR(33) = MRR(18)
MRR(34) = MRR(24)
MRR(35) = MRR(30)
MRR(36) = SIIJ(1,7)
C
IF (T2 .EQ. 0.) GO TO 445
C
MAR( 4) = MAR( 4) + HYQ(1)*SIIJ(2,1) + HYQ(4)*SIIJ(1,2)
MAR( 5) = MAR( 5) + HYQ(2)*SIIJ(2,1) + HYQ(5)*SIIJ(1,2)
MAR( 6) = MAR( 6) + HYQ(3)*SIIJ(2,1) + HYQ(6)*SIIJ(1,2)
MAR(10) = MAR(10) + HYQ(1)*SIIJ(2,2) + HYQ(4)*SIIJ(1,3)
MAR(11) = MAR(11) + HYQ(2)*SIIJ(2,2) + HYQ(5)*SIIJ(1,3)
MAR(12) = MAR(12) + HYQ(3)*SIIJ(2,2) + HYQ(6)*SIIJ(1,3)
MAR(16) = MAR(16) - HYQ(1)*SIIJ(3,1) - HYQ(4)*SIIJ(2,2)
MAR(17) = MAR(17) - HYQ(2)*SIIJ(3,1) - HYQ(5)*SIIJ(2,2)
MAR(18) = MAR(18) - HYQ(3)*SIIJ(3,1) - HYQ(6)*SIIJ(2,2)
MRR( 4) = MRR( 4) + HYQ(1)*SIIJ(4,1) + HYQ(4)*SIIJ(3,2)
MRR( 5) = MRR( 5) + HYQ(2)*SIIJ(4,1) + HYQ(5)*SIIJ(3,2)
MRR( 6) = MRR( 6) + HYQ(3)*SIIJ(4,1) + HYQ(6)*SIIJ(3,2)
MRR(10) = MRR(10) + HYQ(1)*SIIJ(3,2) + HYQ(4)*SIIJ(2,3)
MRR(11) = MRR(11) + HYQ(2)*SIIJ(3,2) + HYQ(5)*SIIJ(2,3)
MRR(12) = MRR(12) + HYQ(3)*SIIJ(3,2) + HYQ(6)*SIIJ(2,3)
MRR(16) = MRR(16) + HYQ(1)*SIIJ(2,3) + HYQ(4)*SIIJ(1,4)
MRR(17) = MRR(17) + HYQ(2)*SIIJ(2,3) + HYQ(5)*SIIJ(1,4)
MRR(18) = MRR(18) + HYQ(3)*SIIJ(2,3) + HYQ(6)*SIIJ(1,4)
MRR(19) = MRR( 4)
MRR(20) = MRR(10)
MRR(21) = MRR(16)
MRR(22) = MRR(22) + HYQ(1)*(HYQ(1)*SIIJ(3,1) + 2.0D0*(SIIJ(5,1) +
1 HYQ(4)*SIIJ(2,2))) + HYQ(4)*(2.0D0*SIIJ(4,2) +
2 HYQ(4)*SIIJ(1,3))
MRR(23) = MRR(23) + HYQ(2)*SIIJ(5,1) + HYQ(5)*SIIJ(4,2) +
1 HYQ(1)*(SIIJ(3,3) + HYQ(2)*SIIJ(3,1) + HYQ(5)*SIIJ(2,2))
2 + HYQ(4)*(SIIJ(2,4) + HYQ(2)*SIIJ(2,2) + HYQ(5)*SIIJ(1,3))
MRR(24) = MRR(24) + HYQ(3)*SIIJ(5,1) + HYQ(6)*SIIJ(4,2) +
1 HYQ(1)*(SIIJ(2,4) + HYQ(3)*SIIJ(3,1) + HYQ(6)*SIIJ(2,2))
2 + HYQ(4)*(SIIJ(1,5) + HYQ(3)*SIIJ(2,2) + HYQ(6)*SIIJ(1,3))
MRR(25) = MRR( 5)
MRR(26) = MRR(11)
MRR(27) = MRR(17)
MRR(28) = MRR(23)
MRR(29) = MRR(29) + HYQ(2)*(HYQ(2)*SIIJ(3,1) + 2.0D0*(SIIJ(3,3) +
1 HYQ(5)*SIIJ(2,2))) + HYQ(5)*(2.0D0*SIIJ(2,4) +
2 HYQ(5)*SIIJ(1,3))
MRR(30) = MRR(30) + HYQ(3)*SIIJ(3,3) + HYQ(6)*SIIJ(2,4) +
1 HYQ(2)*(SIIJ(2,4) + HYQ(3)*SIIJ(3,1) + HYQ(6)*SIIJ(2,2))
2 + HYQ(5)*(SIIJ(1,5) + HYQ(3)*SIIJ(2,2) + HYQ(6)*SIIJ(1,3))
MRR(31) = MRR( 6)
MRR(32) = MRR(12)
MRR(33) = MRR(18)
MRR(34) = MRR(24)
MRR(35) = MRR(30)
MRR(36) = MRR(36) + HYQ(3)*(HYQ(3)*SIIJ(3,1) + 2.0D0*(SIIJ(2,4) +
1 HYQ(6)*SIIJ(2,2))) + HYQ(6)*(2.0D0*SIIJ(1,5) +
2 HYQ(6)*SIIJ(1,3))
C
C FILL S-MATRIX EQUIVALENCED TO A(82) (S IS 6X3 )
C
445 S( 1) = 1.
S( 2) = 0.
S( 3) =-XSUBB
S( 4) = 0.
S( 5) = 1.
S( 6) = 0.
S( 7) = 0.
S( 8) = 0.
S( 9) = 1.
S(10) = 1.
S(11) = YSUBC
S(12) =-XSUBC
S(13) = 0.
S(14) = 1.
S(15) = 0.
S(16) = 0.
S(17) = 0.
S(18) = 1.
C
C CAN NOW COMPUTE 9 (3X3) MASS MATRICES (FMMS-66, PAGES 10-11)
C
C -1 T -1
C ( M ) = ( H ) ( M ) ( H )
C RR
C
C PARTITION (M)
C /// ///
C / * /
C / MBB * MBC /
C / * /
C ( M ) = / ********* /
C / * /
C / MCB * MCC /
C / * /
C /// ///
C 4 (3X3) MATRICES
C -1
C ( M ) = ( M ) ( H )
C AI AR
C
C PARTITION (M ) /// ///
C AI / * /
C ( M ) = / M-BAR-AB * M-BAR-AC /
C AI / * /
C /// ///
C 2 (3X3) MATRICES
C T T
C ( MAB ) = (M-BAR-AB) - (S ) (MBB) - (S ) (MCB)
C B C
C
C T T
C ( MAC ) = (M-BAR-AC) - (S ) (MBC) - (S ) (MCC)
C B C
C
C T T T T
C ( MAA ) = (M-BAR-AA) - (S ) (M ) - (S ) (MAC )
C B AB C
C
C - (M-BAR-AB) (S ) - (M-BAR-AC) (S )
C B C
C
C T
C ( MBA ) = (MAB )
C
C T
C ( MCA ) = (MAC )
C
C CHOOSE APPROPRIATE BLOCK OF A-ARRAY FOR STORAGE
C
C (3X3) STORED IN (3X3) STORED IN (3X3) STORED IN
C (MAA) A( 1... 9) (MAB) A(10)...8) (MAC) A(19...27)
C (MBA) A(28...36) (MBB) A(37)...45) (MBC) A(46...54)
C (MCA) A(55...63) (MCB) A(64...72) (MCC) A(73...81)
C
C -1
C (H ) IS STORED AT A(100...135)
C (S) EQUIVALENCED A( 81... 99)
C WORKING STORAGE IS A(181...216)
C (M-BAR-AB) STORED UNTIL NO LONGER NEEDED IN A(163...171)
C (M-BAR-AC) STORED UNTIL NO LONGER NEEDED IN A(172...180)
C
C -1 T -1
C COMPUTE (M) = (H ) ((M ) (H ))
C RR
C
CALL GMMATD (MRR(1), 6,6,0, A(100), 6,6,0, A(37))
CALL GMMATD (A(100), 6,6,1, A(37), 6,6,0, A(1))
C
C CREATE PARTITION OF 4 (3X3)
C
DO 470 I = 1,3
A(I+36) = A(I )
A(I+39) = A(I+ 6)
A(I+42) = A(I+12)
C
A(I+45) = A(I+ 3)
A(I+48) = A(I+ 9)
A(I+51) = A(I+15)
C
A(I+63) = A(I+18)
A(I+66) = A(I+24)
A(I+69) = A(I+30)
C
A(I+72) = A(I+21)
A(I+75) = A(I+27)
470 A(I+78) = A(I+33)
C
C COMPUTE -1
C (M ) = (M ) (H ) AND PARTITION INTO 2 (3X3) (M-BAR-AB)
C AI AR AND (M-BAR-AC)
C
CALL GMMATD (MAR(1), 3,6,0, A(100), 6,6,0, A(181))
DO 480 I = 1,3
A(I+162) = A(I+180)
A(I+165) = A(I+186)
A(I+168) = A(I+192)
C
A(I+171) = A(I+183)
A(I+174) = A(I+189)
480 A(I+177) = A(I+195)
C
C COMPUTE (MAB)
C
CALL GMMATD (S(1), 3,3,1, A(37), 3,3,0, A(181))
CALL GMMATD (S(10), 3,3,1, A(64), 3,3,0, A(190))
DO 490 I = 1,9
490 A(I+9) = A(I+162) - A(I+180) - A(I+189)
C
C COMPUTE (MAC)
C
CALL GMMATD (S(1) , 3,3,1, A(46), 3,3,0, A(181))
CALL GMMATD (S(10), 3,3,1, A(73), 3,3,0, A(190))
DO 500 I = 1,9
500 A(I+18) = A(I+171) - A(I+180) - A(I+189)
C
C COMPUTE (MAA)
C
CALL GMMATD (S(1) , 3,3,1, A(10), 3,3,1, A(181))
CALL GMMATD (S(10), 3,3,1, A(19), 3,3,1, A(190))
CALL GMMATD (A(163),3,3,0, S(1) , 3,3,0, A(199))
CALL GMMATD (A(172),3,3,0, S(10), 3,3,0, A(208))
DO 510 I = 1,9
510 A(I) = MBARAA(I) - A(I+180) - A(I+189) - A(I+198) - A(I+207)
C
C COMPUTE (MBA) AND (MCA)
C
DO 520 I = 1,3
NPT = 3*I + 7
A(I+27) = A(NPT )
A(I+30) = A(NPT+1)
A(I+33) = A(NPT+2)
C
A(I+54) = A(NPT+ 9)
A(I+57) = A(NPT+10)
520 A(I+60) = A(NPT+11)
C
DO 550 I = 1,136
550 AOUT(I) = A(I)
RETURN
C
C ERROR EXITS
C
600 CALL MESAGE (30,33,ECPT(1))
NOGO = .TRUE.
RETURN
END
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