119. Magic Pairs

time limit per test: 0.25 sec.
memory limit per test: 4096 KB

“Prove that for any integer X and Y if 5X+4Y is divided by 23 than 3X+7Y is divided by 23 too.” The task is from city Olympiad in mathematics in Saratov, Russia for schoolchildren of 8-th form. 2001-2002 year.


For given N and pair (A₀, B₀) find all pairs (A, B) such that for any integer X and Y if A₀X+B₀Y is divided by N then AX+BY is divided by N too (0<=A,B<N).

Input

Each input consists of positive integer numbers N, A_{0 and B0 (N,A0,B0£ 10000) separated by whitespaces.}

Output

Write number of pairs (A, B) to the first line of output. Write each pair on a single line in order of non-descreasing A (and B in case of equal A). Separate numbers by single space.

Sample Input

3
1 2

Sample Output

3 
0 0
1 2
2 1