13:I[87,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"Header"] 14:I[1742,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"ProblemView"] 15:T5e6,

You are given an equation A * X + B * Y = C, A, B, C are positive integer coefficients, X and Y are variables which can have positive integer values only. Output the number of solutions of this equation and the solutions themselves.

Input

The only line of input contains integers A, B and C (1 ≤ A, B, C ≤ 1000), separated with spaces.

Output

In the first line of the output print the number of the solutions N. In the next N lines print the solutions, formatted as "

Diophantine equation

Examples