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B. Find Marble

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputPetya 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.

Examples

Input

4 2 1

2 3 4 1

Output

3

Input

4 3 3

4 1 3 2

Output

0

Input

4 3 4

1 2 3 4

Output

-1

Input

3 1 3

2 1 3

Output

-1

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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