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 "XY", sorted in ascending order of X, one solution per line.

见题面 Input 部分

见题面 Output 部分