/* Objective function */
min: Y;

/* Variable bounds */
x1 >= 0;
x2 >= 0;
x3 >= 0;
x4 >= 0;

y1 >= 0;
y2 >= 0;
y3 >= 0;
y4 >= 0;

x1 + 1 <= 7;
x2 + 5 <= 7;
x3 + 3 <= 7;
x4 + 1 <= 7;

y1 + 3 <= Y;
y2 + 1 <= Y;
y3 + 3 <= Y;
y4 + 5 <= Y;

x1 + 1 <= x2 + 7 x12 + 7 y12;
y1 + 3 <= y2 + 7 + 7 x12 - 7 y12;
x2 + 5 <= x1 + 7 - 7 x12 + 7 y12;
y2 + 1 <= y1 + 14 - 7 x12 - 7 y12;

x1 + 1 <= x3 + 7 x13 + 7 y13;
y1 + 3 <= y3 + 7 + 7 x13 - 7 y13;
x3 + 3 <= x1 + 7 - 7 x13 + 7 y13;
y3 + 3 <= y1 + 14 - 7 x13 - 7 y13;

x1 + 1 <= x4 + 7 x14 + 7 y14;
y1 + 3 <= y4 + 7 + 7 x14 - 7 y14;
x4 + 1 <= x1 + 7 - 7 x14 + 7 y14;
y4 + 5 <= y1 + 14 - 7 x14 - 7 y14;

x2 + 5 <= x3 + 7 x23 + 7 y23;
y2 + 1 <= y3 + 7 + 7 x23 - 7 y23;
x3 + 3 <= x2 + 7 - 7 x23 + 7 y23;
y3 + 3 <= y2 + 14 - 7 x23 - 7 y23;

x2 + 5 <= x4 + 7 x24 + 7 y24;
y2 + 1 <= y4 + 7 + 7 x24 - 7 y24;
x4 + 1 <= x2 + 7 - 7 x24 + 7 y24;
y4 + 5 <= y2 + 14 - 7 x24 - 7 y24;

x3 + 3 <= x4 + 7 x34 + 7 y34;
y3 + 3 <= y4 + 7 + 7 x34 - 7 y34;
x4 + 1 <= x3 + 7 - 7 x34 + 7 y34;
y4 + 5 <= y3 + 14 - 7 x34 - 7 y34;

int x1, x2, x3, x4;
int y1, y2, y3, y4;
bin x12, x13, x14, x23, x24, x34;
bin y12, y13, y14, y23, y24, y34;
int Y;