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ZOJ Problem Set - 2329
AB Circle

Time Limit: 2 Seconds      Memory Limit: 65536 KB

A circle formed by 'a' and 'b', you are required to figure out all such pairs of positions that when cutting the circle in a pair of the positions, we will get two segments that the number of 'a's in one segment is equal to the number of 'b's in the other segment.

Input

The length of circle: n is between 2 and 1000 inclusive.

All the characters in the input is either 'a' or 'b'.

There is no strings without any 'a' in the input.

There is no strings without any 'b' in the input.


Output

There are no more than 400 test cases. For each test case, print out all the correct cuttings. For each cutting, print out a pair of integers, representing the two positions to cut on.

In output, all the pairs of positions should be sorted.

The llegal positions' number is between 0 and n-1 inclusive.

Print a blank line after each test case.


Sample Input

ab
baa


Sample Output

AB Circle #1:
0,1

AB Circle #2:
0,1
0,2
1,2


Note for sample 2

original:     baa
cut in 0,1:
    b    aa
    the number of 'a's in "b" = the number of 'b's in "aa" = 0
cut in 0,2:
    ba    a
    the number of 'b's in "ba" = the number of 'a's in "a" = 1
cut in 1,2:
    a    ab
    the number of 'a's in "a" = the number of 'b's in "ab" = 1

BE CAREFULL: the total size of output might be very large.



Author: ZHENG, Jianqiang
Source: ZOJ 3rd Anniversary Contest
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