ABC Street

ABC Street is a road made of $N$ paving blocks in a row. The blocks are numbered 1 to $N$.

Junseo lives on block 1 and Hayun lives on block $N$. Junseo jumps from block to block to meet Hayun.

Every block has one letter on it, either A, B, or C. The letter on block 1 is always A.

Junseo moves only by jumping, and always toward larger numbers. If he stands on block $i$, he can jump to any block from $i+1$ to $N$. One jump of $k$ blocks costs $k^2$ energy.

Junseo chants A, B, C in that order as he goes. So the letters on the blocks he steps on, starting from the first one, must read A, B, C, A, B, C, and so on.

Write a program that computes the smallest amount of energy Junseo needs to meet Hayun.

The first line contains the number of paving blocks $N$. ($1 \le N \le 1000$)

The second line contains the letters written on blocks 1 to $N$ as one string of length $N$. Each character is A, B, or C, and the first character is always A.

Print the smallest amount of energy Junseo needs to meet Hayun. If he cannot reach Hayun, print -1.

If $N$ is 1, the two of them stand on the same block, so print 0.