Petya and Vasya are playing a game. Petya's got $*n*$ non-transparent glasses, standing in a row. The glasses' positions are indexed with integers from $1$ to $*n*$ from left to right. Note that the positions are indexed but the glasses are not.

First Petya puts a marble under the glass in position $*s*$. Then he performs some (possibly zero) shuffling operations. One shuffling operation means moving the glass from the first position to position $*p*_{1}$, the glass from the second position to position $*p*_{2}$ and so on. That is, a glass goes from position $*i*$ to position $*p*_{*i*}$. Consider all glasses are moving simultaneously during one shuffling operation. When the glasses are shuffled, the marble doesn't travel from one glass to another: it moves together with the glass it was initially been put in.

After all shuffling operations Petya shows Vasya that the ball has moved to position $*t*$. Vasya's task is to say what minimum number of shuffling operations Petya has performed or determine that Petya has made a mistake and the marble could not have got from position $*s*$ to position $*t*$.

Input

The first line contains three integers: $*n*, *s*, *t* (1 ≤ *n* ≤ 10^{5}; 1 ≤ *s*, *t* ≤ *n*)$ — the number of glasses, the ball's initial and final position. The second line contains $*n*$ space-separated integers: $*p*_{1}, *p*_{2}, ..., *p*_{*n*} (1 ≤ *p*_{*i*} ≤ *n*)$ — the shuffling operation parameters. It is guaranteed that all $*p*_{*i*}$'s are distinct.

Note that $*s*$ can equal $*t*$.

Output

If the marble can move from position $*s*$ to position $*t*$, then print on a single line a non-negative integer — the minimum number of shuffling operations, needed to get the marble to position $*t*$. If it is impossible, print number -1.