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Instance waterno1_01

Formats ams gms osil py
Primal Bounds (infeas ≤ 1e-08)
151.05560060 p1 ( gdx sol )
(infeas: 4e-11)
Other points (infeas > 1e-08)  
Dual Bounds
151.05560060 (COUENNE)
151.05560060 (LINDO)
151.05560060 (SCIP)
References Huang, Wei, Operative Planning of Water Supply Networks by Mixed Integer Nonlinear Programming, Masters thesis, Freie Universität Berlin, 2011.
Gleixner, Ambros M, Held, Harald, Huang, Wei, and Vigerske, Stefan, Towards globally optimal operation of water supply networks, Numerical Algebra, Control and Optimization, 2:4, 2012, 695-711.
Application Water Network Operation
Added to library 12 Aug 2014
Problem type MBNLP
#Variables 157
#Binary Variables 15
#Integer Variables 0
#Nonlinear Variables 46
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type linear
Objective curvature linear
#Nonzeros in Objective 12
#Nonlinear Nonzeros in Objective 0
#Constraints 182
#Linear Constraints 136
#Quadratic Constraints 24
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 22
Operands in Gen. Nonlin. Functions signpower
Constraints curvature indefinite
#Nonzeros in Jacobian 471
#Nonlinear Nonzeros in Jacobian 58
#Nonzeros in (Upper-Left) Hessian of Lagrangian 58
#Nonzeros in Diagonal of Hessian of Lagrangian 34
#Blocks in Hessian of Lagrangian 34
Minimal blocksize in Hessian of Lagrangian 1
Maximal blocksize in Hessian of Lagrangian 2
Average blocksize in Hessian of Lagrangian 1.352941
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Minimal coefficient 1.8052e-04
Maximal coefficient 6.0160e+04
Infeasibility of initial point 5796
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
*        183      102       39       42        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*        158      143       15        0        0        0        0        0
*  FX      5
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        484      426       58        0
*
*  Solve m using MINLP minimizing objvar;


Variables  objvar,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,x17,x18
          ,x19,x20,x21,x22,x23,x24,x25,x26,x27,x28,x29,x30,x31,x32,x33,x34,x35
          ,x36,x37,x38,x39,x40,x41,x42,x43,x44,x45,x46,x47,x48,x49,x50,x51,x52
          ,x53,x54,x55,x56,x57,x58,x59,x60,x61,x62,x63,x64,x65,x66,x67,x68,x69
          ,x70,x71,x72,x73,x74,x75,x76,x77,x78,x79,x80,x81,x82,x83,x84,x85,x86
          ,x87,x88,x89,x90,x91,x92,x93,x94,x95,x96,x97,x98,x99,x100,x101,x102
          ,x103,x104,x105,x106,x107,x108,x109,x110,x111,x112,x113,x114,x115
          ,x116,x117,x118,x119,x120,x121,x122,x123,x124,x125,x126,x127,x128
          ,x129,x130,x131,x132,x133,x134,x135,x136,x137,x138,x139,x140,x141
          ,x142,x143,x144,x145,x146,x147,x148,x149,x150,x151,x152,x153,x154
          ,x155,x156,x157,x158;

Positive Variables  x18,x21,x23,x25,x27,x29,x31,x33,x41,x48,x49,x53,x56,x58
          ,x60,x62,x66,x68,x70,x71,x73,x74,x75,x77,x79,x80,x81,x83,x85,x86,x87
          ,x89,x91,x92,x93,x99,x100,x102,x104,x106,x107,x109,x110,x121,x122
          ,x124,x128,x131,x134,x137,x139,x145,x147,x148,x149,x150,x151,x152
          ,x153,x154,x155,x156,x157,x158;

Binary Variables  b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16;

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,e92,e93,e94,e95,e96,e97,e98,e99,e100,e101,e102,e103
          ,e104,e105,e106,e107,e108,e109,e110,e111,e112,e113,e114,e115,e116
          ,e117,e118,e119,e120,e121,e122,e123,e124,e125,e126,e127,e128,e129
          ,e130,e131,e132,e133,e134,e135,e136,e137,e138,e139,e140,e141,e142
          ,e143,e144,e145,e146,e147,e148,e149,e150,e151,e152,e153,e154,e155
          ,e156,e157,e158,e159,e160,e161,e162,e163,e164,e165,e166,e167,e168
          ,e169,e170,e171,e172,e173,e174,e175,e176,e177,e178,e179,e180,e181
          ,e182,e183;


e1..    objvar - x147 - x148 - x149 - x150 - x151 - x152 - x153 - x154 - x155
      - x156 - x157 - x158 =E= 0;

e2..    x72 + x74 =E= 413.764247971;

e3..  - 443.128162372*x76 + x78 + x80 =E= 0;

e4..  - 443.128162372*x82 + x84 + x86 =E= 0;

e5..  - 443.128162372*x88 + x90 + x92 =E= 0;

e6..  - 443.128162372*x94 + x144 + x145 =E= 0;

e7..    x17 + x18 - 443.128162372*x146 =E= 0;

e8..  - 443.128162372*x19 + x20 + x21 =E= 0;

e9..    x22 + x23 =E= 413.764247971;

e10..    x24 + x25 =E= 106.777870451;

e11..    x26 + x27 =E= 106.777870451;

e12..    x28 + x29 =E= 106.777870451;

e13..    x30 + x31 =E= 106.777870452;

e14..  - x32 + x33 =E= 0;

e15..    x32 - x34 - x35 - x36 =E= 0;

e16..    x37 =E= 0.025;

e17..    x38 =E= 0.013;

e18..    x39 + x40 - x41 =E= 0;

e19..    x36 - x39 + x42 - x43 =E= 0;

e20..    x35 - x44 =E= 0;

e21..    x41 + x45 + x46 + x47 - x48 - x49 =E= 0;

e22..  - x37 + x43 + x44 - x50 =E= 0;

e23..  - x38 - x40 + x50 =E= 0;

e24..    x34 - x42 =E= 0;

e25..  - x51 =E= 0.1624;

e26..    x51 - x52 + x53 =E= 0;

e27..    x54 + x55 - x56 =E= 0;

e28..    x56 + x57 - x58 =E= 0;

e29..  - x57 - x59 =E= 0.0138888888888889;

e30..  - x46 + x59 - x60 =E= 0;

e31..    x61 =E= 0;

e32..  - x47 + x58 =E= 0;

e33..  - x45 - x53 =E= 0;

e34..  - x33 + x62 =E= 0;

e35..    3600*x52 + 239.978718892*x63 - 239.978718892*x64 =E= 0;

e36..    3600*x48 - 3600*x54 + 416.560177655*x65 - 416.560177655*x66 =E= 0;

e37..    3600*x49 - 3600*x55 + 416.560177655*x67 - 416.560177655*x68 =E= 0;

e38..    3600*x60 - 3600*x61 + 165.129961038*x69 - 165.129961038*x70 =E= 0;

e39..  - 0.037494*b2 + x71 =G= 0;

e40..  - 0.074997*b3 + x73 =G= 0;

e41..  - 0.074997*b4 + x75 =G= 0;

e42..  - 0.074997*b5 + x77 =G= 0;

e43..  - 0.074997*b6 + x79 =G= 0;

e44..  - 0.074997*b7 + x81 =G= 0;

e45..  - 0.074997*b8 + x83 =G= 0;

e46..  - 0.037494*b9 + x85 =G= 0;

e47..  - 0.097497*b10 + x87 =G= 0;

e48..  - 0.097497*b11 + x89 =G= 0;

e49..  - 0.097497*b12 + x91 =G= 0;

e50..  - 0.058743*b13 + x93 =G= 0;

e51..  - 0.045826*b2 + x71 =L= 0;

e52..  - 0.091663*b3 + x73 =L= 0;

e53..  - 0.091663*b4 + x75 =L= 0;

e54..  - 0.091663*b5 + x77 =L= 0;

e55..  - 0.091663*b6 + x79 =L= 0;

e56..  - 0.091663*b7 + x81 =L= 0;

e57..  - 0.091663*b8 + x83 =L= 0;

e58..  - 0.045826*b9 + x85 =L= 0;

e59..  - 0.119163*b10 + x87 =L= 0;

e60..  - 0.119163*b11 + x89 =L= 0;

e61..  - 0.119163*b12 + x91 =L= 0;

e62..  - 0.071797*b13 + x93 =L= 0;

e63..  - x63 + x95 =E= 300;

e64..  - x65 + x96 =E= 240;

e65..  - x67 + x97 =E= 240;

e66..  - x69 + x98 =E= 243;

e67..    x99 - x100 - x101 =E= 0;

e68..    x100 - x102 - x103 =E= 0;

e69..    x100 - x104 - x105 =E= 0;

e70..    x106 - x107 - x108 =E= 0;

e71..  - x109 + x110 - x111 =E= 0;

e72..    x104 - x109 - x112 =E= 0;

e73..    x100 - x106 - x113 =E= 0;

e74..    x107 - x110 - x114 =E= 0;

e75..    x102 - x104 - x115 =E= 0;

e76..    x104 - x107 - x116 =E= 0;

e77..    x107 - x117 - x118 =E= 0;

e78..    x110 - x119 - x120 =E= 0;

e79..  - x121 + x122 - x123 =E= 0;

e80..  - x124 + x125 - x126 =E= 0;

e81..  - x95 + x124 - x127 =E= 0;

e82..    x96 - x128 - x129 =E= 0;

e83..    x97 - x128 - x130 =E= 0;

e84..  - x131 + x132 - x133 =E= 0;

e85..  - x121 + x134 - x135 =E= 0;

e86..    x132 - x134 - x136 =E= 0;

e87..  - x121 + x137 - x138 =E= 0;

e88..    x98 - x139 - x140 =E= 0;

e89..    x99 - x141 - x142 =E= 0;

e90..  - x128 + x131 - x143 =E= 0;

e91..  - 239.978718892*x63 + 239.978718892*x64 - 416.560177655*x65
       + 416.560177655*x66 - 416.560177655*x67 + 416.560177655*x68
       - 165.129961038*x69 + 165.129961038*x70 =G= 0;

e92..    b2 - b9 =G= 0;

e93..    b3 - b4 =G= 0;

e94..    b4 - b5 =G= 0;

e95..    b5 - b6 =G= 0;

e96..    b6 - b7 =G= 0;

e97..    b7 - b8 =G= 0;

e98..    b10 - b11 =G= 0;

e99..    b11 - b12 =G= 0;

e100..    x33 - x71 - x73 - x75 - x77 - x79 - x81 - x83 - x85 =E= 0;

e101..    x56 - x87 - x89 - x91 - x93 =E= 0;

e102..  - 712.572602172813*b2 + x72 - x142 =G= -712.572602172813;

e103..  - 851.700667228731*b3 + x78 - x142 =G= -851.700667228731;

e104..  - 851.700667228731*b4 + x84 - x142 =G= -851.700667228731;

e105..  - 851.700667228731*b5 + x90 - x142 =G= -851.700667228731;

e106..  - 851.700667228731*b6 - x142 + x144 =G= -851.700667228731;

e107..  - 851.700667228731*b7 + x17 - x142 =G= -851.700667228731;

e108..  - 851.700667228731*b8 + x20 - x142 =G= -851.700667228731;

e109..  - 712.572602172813*b9 + x22 - x142 =G= -712.572602172813;

e110..  - 925.825187656153*b10 + x24 - x143 =G= -925.825187656153;

e111..  - 925.825187656153*b11 + x26 - x143 =G= -925.825187656153;

e112..  - 925.825187656153*b12 + x28 - x143 =G= -925.825187656153;

e113..  - 925.825187656502*b13 + x30 - x143 =G= -925.825187656502;

e114..    447.864247971*b2 + x72 - x142 =L= 447.864247971;

e115..    672.20455381568*b3 + x78 - x142 =L= 672.20455381568;

e116..    672.20455381568*b4 + x84 - x142 =L= 672.20455381568;

e117..    672.20455381568*b5 + x90 - x142 =L= 672.20455381568;

e118..    672.20455381568*b6 - x142 + x144 =L= 672.20455381568;

e119..    672.20455381568*b7 + x17 - x142 =L= 672.20455381568;

e120..    672.20455381568*b8 + x20 - x142 =L= 672.20455381568;

e121..    447.864247971*b9 + x22 - x142 =L= 447.864247971;

e122..    1106.777870451*b10 + x24 - x143 =L= 1106.777870451;

e123..    1106.777870451*b11 + x26 - x143 =L= 1106.777870451;

e124..    1106.777870451*b12 + x28 - x143 =L= 1106.777870451;

e125..    1106.777870452*b13 + x30 - x143 =L= 1106.777870452;

e126..  - 5*b14 + x41 =L= 0;

e127..  - 5*b15 + x58 =L= 0;

e128..  - 5*b16 + x53 =L= 0;

e129..  - 1000*b14 + x109 - x121 =G= -1000;

e130..  - 1000*b15 + x131 - x137 =G= -1000;

e131..  - 1000*b16 + x122 - x124 =G= -1000;

e132..  - 1000*b14 + x109 - x121 =L= 0;

e133..  - 1000*b15 + x131 - x137 =L= 0;

e134..  - 1000*b16 + x122 - x124 =L= 0;

e135..  - x96 + x121 =G= 60;

e136..  - x97 + x121 =G= 60;

e137..  - x98 + x134 =G= 50;

e138.. 60159.7666785*sqr(x71) - x74 =E= 0;

e139.. 16103.4266989*sqr(x73) - x80 =E= 0;

e140.. 16103.4266989*sqr(x75) - x86 =E= 0;

e141.. 16103.4266989*sqr(x77) - x92 =E= 0;

e142.. 16103.4266989*sqr(x79) - x145 =E= 0;

e143.. 16103.4266989*sqr(x81) - x18 =E= 0;

e144.. 16103.4266989*sqr(x83) - x21 =E= 0;

e145.. 60159.7666785*sqr(x85) - x23 =E= 0;

e146.. 2296.01902001*sqr(x87) - x25 =E= 0;

e147.. 2296.01902001*sqr(x89) - x27 =E= 0;

e148.. 2296.01902001*sqr(x91) - x29 =E= 0;

e149.. 6324.78464025*sqr(x93) - x31 =E= 0;

e150.. 2.4525*x71*x72 - x147 =L= 0;

e151.. 2.4525*x73*x78 - x148 =L= 0;

e152.. 2.4525*x75*x84 - x149 =L= 0;

e153.. 2.4525*x77*x90 - x150 =L= 0;

e154.. 2.4525*x79*x144 - x151 =L= 0;

e155.. 2.4525*x17*x81 - x152 =L= 0;

e156.. 2.4525*x20*x83 - x153 =L= 0;

e157.. 2.4525*x22*x85 - x154 =L= 0;

e158.. 2.4525*x24*x87 - x155 =L= 0;

e159.. 2.4525*x26*x89 - x156 =L= 0;

e160.. 2.4525*x28*x91 - x157 =L= 0;

e161.. 2.4525*x30*x93 - x158 =L= 0;

e162.. SignPower(x32,2) - 0.107595782151047*x101 =E= 0;

e163.. SignPower(x34,2) - 0.000240846101592208*x103 =E= 0;

e164.. SignPower(x36,2) - 0.0011039398274554*x105 =E= 0;

e165.. SignPower(x44,2) - 0.0147658094299242*x108 =E= 0;

e166.. SignPower(x40,2) - 0.0126524872624481*x111 =E= 0;

e167.. SignPower(x39,2) - 0.000713164667292268*x112 =E= 0;

e168.. SignPower(x35,2) - 0.0253049745248962*x113 =E= 0;

e169.. SignPower(x50,2) - 0.0196735206566467*x114 =E= 0;

e170.. SignPower(x42,2) - 0.13436247753087*x115 =E= 0;

e171.. SignPower(x43,2) - 0.13436247753087*x116 =E= 0;

e172.. SignPower(x37,2) - 0.00268724955062101*x118 =E= 0;

e173.. SignPower(x38,2) - 0.00175817654162355*x120 =E= 0;

e174.. SignPower(x45,2) - 0.0156579704750926*x123 =E= 0;

e175.. SignPower(x51,2) - 0.4031634796292*x126 =E= 0;

e176.. SignPower(x52,2) - 0.4031634796292*x127 =E= 0;

e177.. SignPower(x54,2) - 8.06326959261651*x129 =E= 0;

e178.. SignPower(x55,2) - 8.06326959261651*x130 =E= 0;

e179.. SignPower(x57,2) - 0.000180519501834947*x133 =E= 0;

e180.. SignPower(x46,2) - 0.000180519501834947*x135 =E= 0;

e181.. SignPower(x59,2) - 0.013538962637621*x136 =E= 0;

e182.. SignPower(x47,2) - 0.0463936827608069*x138 =E= 0;

e183.. SignPower(x61,2) - 0.0964450219247959*x140 =E= 0;

* set non-default bounds
x17.lo = 148.299332771269; x17.up = 638.10455381568;
x18.up = 135.302691146811;
x19.lo = 0.8; x19.up = 1.2;
x20.lo = 148.299332771269; x20.up = 638.10455381568;
x21.up = 135.302691146811;
x22.lo = 287.427397827187; x22.up = 413.764247971;
x23.up = 126.336850143813;
x24.lo = 74.1748123438468; x24.up = 106.777870451;
x25.up = 32.6030581071532;
x26.lo = 74.1748123438468; x26.up = 106.777870451;
x27.up = 32.6030581071532;
x28.lo = 74.1748123438468; x28.up = 106.777870451;
x29.up = 32.6030581071532;
x30.lo = 74.1748123434975; x30.up = 106.777870452;
x31.up = 32.6030581085025;
x32.lo = -5; x32.up = 5;
x33.up = 0.64163;
x34.lo = -5; x34.up = 5;
x35.lo = -5; x35.up = 5;
x36.lo = -5; x36.up = 5;
x37.lo = -5; x37.up = 5;
x38.lo = -5; x38.up = 5;
x39.lo = -5; x39.up = 5;
x40.lo = -5; x40.up = 5;
x41.up = 5;
x42.lo = -5; x42.up = 5;
x43.lo = -5; x43.up = 5;
x44.lo = -5; x44.up = 5;
x45.lo = -5; x45.up = 5;
x46.lo = -5; x46.up = 5;
x47.lo = -5; x47.up = 5;
x48.up = 5;
x49.up = 5;
x50.lo = -5; x50.up = 5;
x51.lo = -5; x51.up = 5;
x52.lo = -5; x52.up = 5;
x53.up = 5;
x54.lo = -5; x54.up = 5;
x55.lo = -5; x55.up = 5;
x56.up = 0.429286;
x57.lo = -5; x57.up = 5;
x58.up = 5;
x59.lo = -5; x59.up = 5;
x60.up = 5;
x61.lo = -5; x61.up = 5;
x62.up = 5;
x63.fx = 6.3;
x64.lo = 5; x64.up = 10;
x65.fx = 4.6;
x66.up = 6;
x67.fx = 4.6;
x68.up = 6;
x69.fx = 10;
x70.up = 16.5;
x71.up = 0.045826;
x72.lo = 287.427397827187; x72.up = 413.764247971;
x73.up = 0.091663;
x74.up = 126.336850143813;
x75.up = 0.091663;
x76.lo = 0.8; x76.up = 1.2;
x77.up = 0.091663;
x78.lo = 148.299332771269; x78.up = 638.10455381568;
x79.up = 0.091663;
x80.up = 135.302691146811;
x81.up = 0.091663;
x82.lo = 0.8; x82.up = 1.2;
x83.up = 0.091663;
x84.lo = 148.299332771269; x84.up = 638.10455381568;
x85.up = 0.045826;
x86.up = 135.302691146811;
x87.up = 0.119163;
x88.lo = 0.8; x88.up = 1.2;
x89.up = 0.119163;
x90.lo = 148.299332771269; x90.up = 638.10455381568;
x91.up = 0.119163;
x92.up = 135.302691146811;
x93.up = 0.071797;
x94.lo = 0.8; x94.up = 1.2;
x95.lo = 305; x95.up = 310;
x96.lo = 240; x96.up = 246;
x97.lo = 240; x97.up = 246;
x98.lo = 243; x98.up = 259.5;
x99.up = 1000;
x100.up = 1000;
x101.lo = -232.35111544525; x101.up = 232.35111544525;
x102.up = 1000;
x103.lo = -103800.7251715; x103.up = 103800.7251715;
x104.up = 1000;
x105.lo = -22646.161845275; x105.up = 22646.161845275;
x106.up = 1000;
x107.up = 1000;
x108.lo = -1693.1005454625; x108.up = 1693.1005454625;
x109.up = 1000;
x110.up = 1000;
x111.lo = -1975.896081255; x111.up = 1975.896081255;
x112.lo = -35055.017651; x112.up = 35055.017651;
x113.lo = -987.9480406275; x113.up = 987.9480406275;
x114.lo = -1270.74357642; x114.up = 1270.74357642;
x115.lo = -186.06385100525; x115.up = 186.06385100525;
x116.lo = -186.06385100525; x116.up = 186.06385100525;
x117.lo = 214.9; x117.up = 1000;
x118.lo = -9303.19255025; x118.up = 9303.19255025;
x119.lo = 231.04; x119.up = 1000;
x120.lo = -14219.27742075; x120.up = 14219.27742075;
x121.up = 1000;
x122.up = 1000;
x123.lo = -1596.630932455; x123.up = 1596.630932455;
x124.up = 1000;
x125.lo = 300; x125.up = 1000;
x126.lo = -62.00958485375; x126.up = 62.00958485375;
x127.lo = -62.00958485375; x127.up = 62.00958485375;
x128.up = 1000;
x129.lo = -3.100479242675; x129.up = 3.100479242675;
x130.lo = -3.100479242675; x130.up = 3.100479242675;
x131.up = 1000;
x132.lo = 243; x132.up = 1000;
x133.lo = -138489.1922805; x133.up = 138489.1922805;
x134.up = 1000;
x135.lo = -138489.1922805; x135.up = 138489.1922805;
x136.lo = -1846.52256374; x136.up = 1846.52256374;
x137.up = 1000;
x138.lo = -538.866468715; x138.up = 538.866468715;
x139.up = 1000;
x140.lo = -259.21503776; x140.up = 259.21503776;
x141.fx = 34.1;
x142.lo = -34.1; x142.up = 1000;
x143.lo = -1000; x143.up = 1000;
x144.lo = 148.299332771269; x144.up = 638.10455381568;
x145.up = 135.302691146811;
x146.lo = 0.8; x146.up = 1.2;
x147.up = 46.5022459484905;
x148.up = 143.448141849487;
x149.up = 143.448141849487;
x150.up = 143.448141849487;
x151.up = 143.448141849487;
x152.up = 143.448141849487;
x153.up = 143.448141849487;
x154.up = 46.5022459484905;
x155.up = 31.205539800995;
x156.up = 31.205539800995;
x157.up = 31.205539800995;
x158.up = 18.8016762007756;

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: 2022-04-26 Git hash: de668763
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