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Instance tls5

Formatsⓘ ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)ⓘ
14.40000000 p1 ( gdx sol )
(infeas: 0)
14.20000000 p2 ( gdx sol )
(infeas: 0)
11.50000000 p3 ( gdx sol )
(infeas: 0)
10.30000000 p4 ( gdx sol )
(infeas: 0)
Other points (infeas > 1e-08)ⓘ  
Dual Boundsⓘ
5.90000000 (ALPHAECP)
8.37000184 (ANTIGONE)
9.20000000 (BARON)
5.58604248 (BONMIN)
1.19372783 (COUENNE)
10.30000000 (GUROBI)
6.43333333 (LINDO)
7.70000000 (SCIP)
7.70735569 (SHOT)
8.90000000 (XPRESS)
Referencesⓘ Harjunkoski, Iiro, Westerlund, Tapio, Pörn, Ray, and Skrifvars, Hans, Different Transformations for Solving Non-Convex Trim Loss Problems by MINLP, European Journal of Operational Research, 105:3, 1998, 594-603.
Sourceⓘ MacMINLP model trimlon.mod with trimloss2.dat
Applicationⓘ Trim loss minimization problem
Added to libraryⓘ 01 May 2001
Problem typeⓘ MINLP
#Variablesⓘ 161
#Binary Variablesⓘ 131
#Integer Variablesⓘ 5
#Nonlinear Variablesⓘ 30
#Nonlinear Binary Variablesⓘ 0
#Nonlinear Integer Variablesⓘ 5
Objective Senseⓘ min
Objective typeⓘ linear
Objective curvatureⓘ linear
#Nonzeros in Objectiveⓘ 31
#Nonlinear Nonzeros in Objectiveⓘ 0
#Constraintsⓘ 90
#Linear Constraintsⓘ 85
#Quadratic Constraintsⓘ 0
#Polynomial Constraintsⓘ 0
#Signomial Constraintsⓘ 5
#General Nonlinear Constraintsⓘ 0
Operands in Gen. Nonlin. Functionsⓘ  
Constraints curvatureⓘ convex
#Nonzeros in Jacobianⓘ 924
#Nonlinear Nonzeros in Jacobianⓘ 50
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ 80
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ 30
#Blocks in Hessian of Lagrangianⓘ 5
Minimal blocksize in Hessian of Lagrangianⓘ 6
Maximal blocksize in Hessian of Lagrangianⓘ 6
Average blocksize in Hessian of Lagrangianⓘ 6.0
#Semicontinuitiesⓘ 0
#Nonlinear Semicontinuitiesⓘ 0
#SOS type 1ⓘ 0
#SOS type 2ⓘ 0
Minimal coefficientⓘ 1.0000e-01
Maximal coefficientⓘ 1.8500e+03
Infeasibility of initial pointⓘ 1800
Sparsity Jacobianⓘ Sparsity of Objective Gradient and Jacobian
Sparsity Hessian of Lagrangianⓘ Sparsity of Hessian of Lagrangian 
$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*         91       31        0       60        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*        162       26      131        5        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        956      906       50        0
*
*  Solve m using MINLP minimizing objvar;


Variables  b1,b2,b3,b4,b5,i6,i7,i8,i9,i10,x11,x12,x13,x14,x15,x16,x17,x18,x19
          ,x20,x21,x22,x23,x24,x25,x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,b36
          ,b37,b38,b39,b40,b41,b42,b43,b44,b45,b46,b47,b48,b49,b50,b51,b52,b53
          ,b54,b55,b56,b57,b58,b59,b60,b61,b62,b63,b64,b65,b66,b67,b68,b69,b70
          ,b71,b72,b73,b74,b75,b76,b77,b78,b79,b80,b81,b82,b83,b84,b85,b86,b87
          ,b88,b89,b90,b91,b92,b93,b94,b95,b96,b97,b98,b99,b100,b101,b102,b103
          ,b104,b105,b106,b107,b108,b109,b110,b111,b112,b113,b114,b115,b116
          ,b117,b118,b119,b120,b121,b122,b123,b124,b125,b126,b127,b128,b129
          ,b130,b131,b132,b133,b134,b135,b136,b137,b138,b139,b140,b141,b142
          ,b143,b144,b145,b146,b147,b148,b149,b150,b151,b152,b153,b154,b155
          ,b156,b157,b158,b159,b160,b161,objvar;

Binary Variables  b1,b2,b3,b4,b5,b36,b37,b38,b39,b40,b41,b42,b43,b44,b45,b46
          ,b47,b48,b49,b50,b51,b52,b53,b54,b55,b56,b57,b58,b59,b60,b61,b62,b63
          ,b64,b65,b66,b67,b68,b69,b70,b71,b72,b73,b74,b75,b76,b77,b78,b79,b80
          ,b81,b82,b83,b84,b85,b86,b87,b88,b89,b90,b91,b92,b93,b94,b95,b96,b97
          ,b98,b99,b100,b101,b102,b103,b104,b105,b106,b107,b108,b109,b110,b111
          ,b112,b113,b114,b115,b116,b117,b118,b119,b120,b121,b122,b123,b124
          ,b125,b126,b127,b128,b129,b130,b131,b132,b133,b134,b135,b136,b137
          ,b138,b139,b140,b141,b142,b143,b144,b145,b146,b147,b148,b149,b150
          ,b151,b152,b153,b154,b155,b156,b157,b158,b159,b160,b161;

Integer Variables  i6,i7,i8,i9,i10;

Equations  e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13,e14,e15,e16,e17,e18,e19
          ,e20,e21,e22,e23,e24,e25,e26,e27,e28,e29,e30,e31,e32,e33,e34,e35,e36
          ,e37,e38,e39,e40,e41,e42,e43,e44,e45,e46,e47,e48,e49,e50,e51,e52,e53
          ,e54,e55,e56,e57,e58,e59,e60,e61,e62,e63,e64,e65,e66,e67,e68,e69,e70
          ,e71,e72,e73,e74,e75,e76,e77,e78,e79,e80,e81,e82,e83,e84,e85,e86,e87
          ,e88,e89,e90,e91;


e1..  - 0.1*b1 - 0.2*b2 - 0.3*b3 - 0.4*b4 - 0.5*b5 - b36 - 2*b37 - 3*b38
      - 4*b39 - 5*b40 - 6*b41 - 7*b42 - 8*b43 - 9*b44 - b45 - 2*b46 - 3*b47
      - 4*b48 - 5*b49 - 6*b50 - b51 - 2*b52 - 3*b53 - 4*b54 - 5*b55 - 6*b56
      - b57 - 2*b58 - 3*b59 - b60 - 2*b61 + objvar =E= 0;

e2..    330*b62 + 660*b63 + 990*b64 + 360*b77 + 720*b78 + 1080*b79 + 1440*b80
      + 1800*b81 + 370*b102 + 740*b103 + 1110*b104 + 1480*b105 + 1850*b106
      + 415*b127 + 830*b128 + 1245*b129 + 1660*b130 + 435*b147 + 870*b148
      + 1305*b149 =L= 2000;

e3..    330*b65 + 660*b66 + 990*b67 + 360*b82 + 720*b83 + 1080*b84 + 1440*b85
      + 1800*b86 + 370*b107 + 740*b108 + 1110*b109 + 1480*b110 + 1850*b111
      + 415*b131 + 830*b132 + 1245*b133 + 1660*b134 + 435*b150 + 870*b151
      + 1305*b152 =L= 2000;

e4..    330*b68 + 660*b69 + 990*b70 + 360*b87 + 720*b88 + 1080*b89 + 1440*b90
      + 1800*b91 + 370*b112 + 740*b113 + 1110*b114 + 1480*b115 + 1850*b116
      + 415*b135 + 830*b136 + 1245*b137 + 1660*b138 + 435*b153 + 870*b154
      + 1305*b155 =L= 2000;

e5..    330*b71 + 660*b72 + 990*b73 + 360*b92 + 720*b93 + 1080*b94 + 1440*b95
      + 1800*b96 + 370*b117 + 740*b118 + 1110*b119 + 1480*b120 + 1850*b121
      + 415*b139 + 830*b140 + 1245*b141 + 1660*b142 + 435*b156 + 870*b157
      + 1305*b158 =L= 2000;

e6..    330*b74 + 660*b75 + 990*b76 + 360*b97 + 720*b98 + 1080*b99 + 1440*b100
      + 1800*b101 + 370*b122 + 740*b123 + 1110*b124 + 1480*b125 + 1850*b126
      + 415*b143 + 830*b144 + 1245*b145 + 1660*b146 + 435*b159 + 870*b160
      + 1305*b161 =L= 2000;

e7..  - 330*b62 - 660*b63 - 990*b64 - 360*b77 - 720*b78 - 1080*b79 - 1440*b80
      - 1800*b81 - 370*b102 - 740*b103 - 1110*b104 - 1480*b105 - 1850*b106
      - 415*b127 - 830*b128 - 1245*b129 - 1660*b130 - 435*b147 - 870*b148
      - 1305*b149 =L= -1800;

e8..  - 330*b65 - 660*b66 - 990*b67 - 360*b82 - 720*b83 - 1080*b84 - 1440*b85
      - 1800*b86 - 370*b107 - 740*b108 - 1110*b109 - 1480*b110 - 1850*b111
      - 415*b131 - 830*b132 - 1245*b133 - 1660*b134 - 435*b150 - 870*b151
      - 1305*b152 =L= -1800;

e9..  - 330*b68 - 660*b69 - 990*b70 - 360*b87 - 720*b88 - 1080*b89 - 1440*b90
      - 1800*b91 - 370*b112 - 740*b113 - 1110*b114 - 1480*b115 - 1850*b116
      - 415*b135 - 830*b136 - 1245*b137 - 1660*b138 - 435*b153 - 870*b154
      - 1305*b155 =L= -1800;

e10..  - 330*b71 - 660*b72 - 990*b73 - 360*b92 - 720*b93 - 1080*b94 - 1440*b95
       - 1800*b96 - 370*b117 - 740*b118 - 1110*b119 - 1480*b120 - 1850*b121
       - 415*b139 - 830*b140 - 1245*b141 - 1660*b142 - 435*b156 - 870*b157
       - 1305*b158 =L= -1800;

e11..  - 330*b74 - 660*b75 - 990*b76 - 360*b97 - 720*b98 - 1080*b99 - 1440*b100
       - 1800*b101 - 370*b122 - 740*b123 - 1110*b124 - 1480*b125 - 1850*b126
       - 415*b143 - 830*b144 - 1245*b145 - 1660*b146 - 435*b159 - 870*b160
       - 1305*b161 =L= -1800;

e12..    b62 + 2*b63 + 3*b64 + b77 + 2*b78 + 3*b79 + 4*b80 + 5*b81 + b102
       + 2*b103 + 3*b104 + 4*b105 + 5*b106 + b127 + 2*b128 + 3*b129 + 4*b130
       + b147 + 2*b148 + 3*b149 =L= 5;

e13..    b65 + 2*b66 + 3*b67 + b82 + 2*b83 + 3*b84 + 4*b85 + 5*b86 + b107
       + 2*b108 + 3*b109 + 4*b110 + 5*b111 + b131 + 2*b132 + 3*b133 + 4*b134
       + b150 + 2*b151 + 3*b152 =L= 5;

e14..    b68 + 2*b69 + 3*b70 + b87 + 2*b88 + 3*b89 + 4*b90 + 5*b91 + b112
       + 2*b113 + 3*b114 + 4*b115 + 5*b116 + b135 + 2*b136 + 3*b137 + 4*b138
       + b153 + 2*b154 + 3*b155 =L= 5;

e15..    b71 + 2*b72 + 3*b73 + b92 + 2*b93 + 3*b94 + 4*b95 + 5*b96 + b117
       + 2*b118 + 3*b119 + 4*b120 + 5*b121 + b139 + 2*b140 + 3*b141 + 4*b142
       + b156 + 2*b157 + 3*b158 =L= 5;

e16..    b74 + 2*b75 + 3*b76 + b97 + 2*b98 + 3*b99 + 4*b100 + 5*b101 + b122
       + 2*b123 + 3*b124 + 4*b125 + 5*b126 + b143 + 2*b144 + 3*b145 + 4*b146
       + b159 + 2*b160 + 3*b161 =L= 5;

e17..    b1 - b36 - 2*b37 - 3*b38 - 4*b39 - 5*b40 - 6*b41 - 7*b42 - 8*b43
       - 9*b44 =L= 0;

e18..    b2 - b45 - 2*b46 - 3*b47 - 4*b48 - 5*b49 - 6*b50 =L= 0;

e19..    b3 - b51 - 2*b52 - 3*b53 - 4*b54 - 5*b55 - 6*b56 =L= 0;

e20..    b4 - b57 - 2*b58 - 3*b59 =L= 0;

e21..    b5 - b60 - 2*b61 =L= 0;

e22..  - 9*b1 + b36 + 2*b37 + 3*b38 + 4*b39 + 5*b40 + 6*b41 + 7*b42 + 8*b43
       + 9*b44 =L= 0;

e23..  - 6*b2 + b45 + 2*b46 + 3*b47 + 4*b48 + 5*b49 + 6*b50 =L= 0;

e24..  - 6*b3 + b51 + 2*b52 + 3*b53 + 4*b54 + 5*b55 + 6*b56 =L= 0;

e25..  - 3*b4 + b57 + 2*b58 + 3*b59 =L= 0;

e26..  - 2*b5 + b60 + 2*b61 =L= 0;

e27..    i6 - 3*b36 - 8*b37 - 15*b38 - 24*b39 - 35*b40 - 48*b41 - 63*b42
       - 80*b43 - 99*b44 =E= 1;

e28..    i7 - 3*b45 - 8*b46 - 15*b47 - 24*b48 - 35*b49 - 48*b50 =E= 1;

e29..    i8 - 3*b51 - 8*b52 - 15*b53 - 24*b54 - 35*b55 - 48*b56 =E= 1;

e30..    i9 - 3*b57 - 8*b58 - 15*b59 =E= 1;

e31..    i10 - 3*b60 - 8*b61 =E= 1;

e32..    b36 + b37 + b38 + b39 + b40 + b41 + b42 + b43 + b44 =L= 1;

e33..    b45 + b46 + b47 + b48 + b49 + b50 =L= 1;

e34..    b51 + b52 + b53 + b54 + b55 + b56 =L= 1;

e35..    b57 + b58 + b59 =L= 1;

e36..    b60 + b61 =L= 1;

e37..    x11 - 3*b62 - 8*b63 - 15*b64 =E= 1;

e38..    x12 - 3*b65 - 8*b66 - 15*b67 =E= 1;

e39..    x13 - 3*b68 - 8*b69 - 15*b70 =E= 1;

e40..    x14 - 3*b71 - 8*b72 - 15*b73 =E= 1;

e41..    x15 - 3*b74 - 8*b75 - 15*b76 =E= 1;

e42..    x16 - 3*b77 - 8*b78 - 15*b79 - 24*b80 - 35*b81 =E= 1;

e43..    x17 - 3*b82 - 8*b83 - 15*b84 - 24*b85 - 35*b86 =E= 1;

e44..    x18 - 3*b87 - 8*b88 - 15*b89 - 24*b90 - 35*b91 =E= 1;

e45..    x19 - 3*b92 - 8*b93 - 15*b94 - 24*b95 - 35*b96 =E= 1;

e46..    x20 - 3*b97 - 8*b98 - 15*b99 - 24*b100 - 35*b101 =E= 1;

e47..    x21 - 3*b102 - 8*b103 - 15*b104 - 24*b105 - 35*b106 =E= 1;

e48..    x22 - 3*b107 - 8*b108 - 15*b109 - 24*b110 - 35*b111 =E= 1;

e49..    x23 - 3*b112 - 8*b113 - 15*b114 - 24*b115 - 35*b116 =E= 1;

e50..    x24 - 3*b117 - 8*b118 - 15*b119 - 24*b120 - 35*b121 =E= 1;

e51..    x25 - 3*b122 - 8*b123 - 15*b124 - 24*b125 - 35*b126 =E= 1;

e52..    x26 - 3*b127 - 8*b128 - 15*b129 - 24*b130 =E= 1;

e53..    x27 - 3*b131 - 8*b132 - 15*b133 - 24*b134 =E= 1;

e54..    x28 - 3*b135 - 8*b136 - 15*b137 - 24*b138 =E= 1;

e55..    x29 - 3*b139 - 8*b140 - 15*b141 - 24*b142 =E= 1;

e56..    x30 - 3*b143 - 8*b144 - 15*b145 - 24*b146 =E= 1;

e57..    x31 - 3*b147 - 8*b148 - 15*b149 =E= 1;

e58..    x32 - 3*b150 - 8*b151 - 15*b152 =E= 1;

e59..    x33 - 3*b153 - 8*b154 - 15*b155 =E= 1;

e60..    x34 - 3*b156 - 8*b157 - 15*b158 =E= 1;

e61..    x35 - 3*b159 - 8*b160 - 15*b161 =E= 1;

e62..    b62 + b63 + b64 =L= 1;

e63..    b65 + b66 + b67 =L= 1;

e64..    b68 + b69 + b70 =L= 1;

e65..    b71 + b72 + b73 =L= 1;

e66..    b74 + b75 + b76 =L= 1;

e67..    b77 + b78 + b79 + b80 + b81 =L= 1;

e68..    b82 + b83 + b84 + b85 + b86 =L= 1;

e69..    b87 + b88 + b89 + b90 + b91 =L= 1;

e70..    b92 + b93 + b94 + b95 + b96 =L= 1;

e71..    b97 + b98 + b99 + b100 + b101 =L= 1;

e72..    b102 + b103 + b104 + b105 + b106 =L= 1;

e73..    b107 + b108 + b109 + b110 + b111 =L= 1;

e74..    b112 + b113 + b114 + b115 + b116 =L= 1;

e75..    b117 + b118 + b119 + b120 + b121 =L= 1;

e76..    b122 + b123 + b124 + b125 + b126 =L= 1;

e77..    b127 + b128 + b129 + b130 =L= 1;

e78..    b131 + b132 + b133 + b134 =L= 1;

e79..    b135 + b136 + b137 + b138 =L= 1;

e80..    b139 + b140 + b141 + b142 =L= 1;

e81..    b143 + b144 + b145 + b146 =L= 1;

e82..    b147 + b148 + b149 =L= 1;

e83..    b150 + b151 + b152 =L= 1;

e84..    b153 + b154 + b155 =L= 1;

e85..    b156 + b157 + b158 =L= 1;

e86..    b159 + b160 + b161 =L= 1;

e87.. -(sqrt(i6*x11) + sqrt(i7*x12) + sqrt(i8*x13) + sqrt(i9*x14) + sqrt(i10*
      x15)) + b36 + 2*b37 + 3*b38 + 4*b39 + 5*b40 + 6*b41 + 7*b42 + 8*b43
       + 9*b44 + b45 + 2*b46 + 3*b47 + 4*b48 + 5*b49 + 6*b50 + b51 + 2*b52
       + 3*b53 + 4*b54 + 5*b55 + 6*b56 + b57 + 2*b58 + 3*b59 + b60 + 2*b61
       + b62 + 2*b63 + 3*b64 + b65 + 2*b66 + 3*b67 + b68 + 2*b69 + 3*b70 + b71
       + 2*b72 + 3*b73 + b74 + 2*b75 + 3*b76 =L= -17;

e88.. -(sqrt(i6*x16) + sqrt(i7*x17) + sqrt(i8*x18) + sqrt(i9*x19) + sqrt(i10*
      x20)) + b36 + 2*b37 + 3*b38 + 4*b39 + 5*b40 + 6*b41 + 7*b42 + 8*b43
       + 9*b44 + b45 + 2*b46 + 3*b47 + 4*b48 + 5*b49 + 6*b50 + b51 + 2*b52
       + 3*b53 + 4*b54 + 5*b55 + 6*b56 + b57 + 2*b58 + 3*b59 + b60 + 2*b61
       + b77 + 2*b78 + 3*b79 + 4*b80 + 5*b81 + b82 + 2*b83 + 3*b84 + 4*b85
       + 5*b86 + b87 + 2*b88 + 3*b89 + 4*b90 + 5*b91 + b92 + 2*b93 + 3*b94
       + 4*b95 + 5*b96 + b97 + 2*b98 + 3*b99 + 4*b100 + 5*b101 =L= -11;

e89.. -(sqrt(i6*x21) + sqrt(i7*x22) + sqrt(i8*x23) + sqrt(i9*x24) + sqrt(i10*
      x25)) + b36 + 2*b37 + 3*b38 + 4*b39 + 5*b40 + 6*b41 + 7*b42 + 8*b43
       + 9*b44 + b45 + 2*b46 + 3*b47 + 4*b48 + 5*b49 + 6*b50 + b51 + 2*b52
       + 3*b53 + 4*b54 + 5*b55 + 6*b56 + b57 + 2*b58 + 3*b59 + b60 + 2*b61
       + b102 + 2*b103 + 3*b104 + 4*b105 + 5*b106 + b107 + 2*b108 + 3*b109
       + 4*b110 + 5*b111 + b112 + 2*b113 + 3*b114 + 4*b115 + 5*b116 + b117
       + 2*b118 + 3*b119 + 4*b120 + 5*b121 + b122 + 2*b123 + 3*b124 + 4*b125
       + 5*b126 =L= -20;

e90.. -(sqrt(i6*x26) + sqrt(i7*x27) + sqrt(i8*x28) + sqrt(i9*x29) + sqrt(i10*
      x30)) + b36 + 2*b37 + 3*b38 + 4*b39 + 5*b40 + 6*b41 + 7*b42 + 8*b43
       + 9*b44 + b45 + 2*b46 + 3*b47 + 4*b48 + 5*b49 + 6*b50 + b51 + 2*b52
       + 3*b53 + 4*b54 + 5*b55 + 6*b56 + b57 + 2*b58 + 3*b59 + b60 + 2*b61
       + b127 + 2*b128 + 3*b129 + 4*b130 + b131 + 2*b132 + 3*b133 + 4*b134
       + b135 + 2*b136 + 3*b137 + 4*b138 + b139 + 2*b140 + 3*b141 + 4*b142
       + b143 + 2*b144 + 3*b145 + 4*b146 =L= -11;

e91.. -(sqrt(i6*x31) + sqrt(i7*x32) + sqrt(i8*x33) + sqrt(i9*x34) + sqrt(i10*
      x35)) + b36 + 2*b37 + 3*b38 + 4*b39 + 5*b40 + 6*b41 + 7*b42 + 8*b43
       + 9*b44 + b45 + 2*b46 + 3*b47 + 4*b48 + 5*b49 + 6*b50 + b51 + 2*b52
       + 3*b53 + 4*b54 + 5*b55 + 6*b56 + b57 + 2*b58 + 3*b59 + b60 + 2*b61
       + b147 + 2*b148 + 3*b149 + b150 + 2*b151 + 3*b152 + b153 + 2*b154
       + 3*b155 + b156 + 2*b157 + 3*b158 + b159 + 2*b160 + 3*b161 =L= -14;

* set non-default bounds
i6.lo = 1; i6.up = 100;
i7.lo = 1; i7.up = 100;
i8.lo = 1; i8.up = 100;
i9.lo = 1; i9.up = 100;
i10.lo = 1; i10.up = 100;
x11.lo = 1;
x12.lo = 1;
x13.lo = 1;
x14.lo = 1;
x15.lo = 1;
x16.lo = 1;
x17.lo = 1;
x18.lo = 1;
x19.lo = 1;
x20.lo = 1;
x21.lo = 1;
x22.lo = 1;
x23.lo = 1;
x24.lo = 1;
x25.lo = 1;
x26.lo = 1;
x27.lo = 1;
x28.lo = 1;
x29.lo = 1;
x30.lo = 1;
x31.lo = 1;
x32.lo = 1;
x33.lo = 1;
x34.lo = 1;
x35.lo = 1;

Model m / all /;

m.limrow=0; m.limcol=0;
m.tolproj=0.0;

$if NOT '%gams.u1%' == '' $include '%gams.u1%'

$if not set MINLP $set MINLP MINLP
Solve m using %MINLP% minimizing objvar;
Last updated: 2025-08-07 Git hash: e62cedfc
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