Hopscotch Addict

Ken loves ken-ken-pa (Japanese version of hopscotch). Today, he will play it on a directed graph G. G consists of N vertices numbered 1 to N, and M edges. The i-th edge points from Vertex u_i to Vertex v_i.

First, Ken stands on Vertex S. He wants to reach Vertex T by repeating ken-ken-pa. In one ken-ken-pa, he does the following exactly three times: follow an edge pointing from the vertex on which he is standing.

Determine if he can reach Vertex T by repeating ken-ken-pa. If the answer is yes, find the minimum number of ken-ken-pa needed to reach Vertex T. Note that visiting Vertex T in the middle of a ken-ken-pa does not count as reaching Vertex T by repeating ken-ken-pa.

Constraints

• 2 \leq N \leq 10^5
• 0 \leq M \leq \min(10^5, N (N-1))
• 1 \leq u_i, v_i \leq N(1 \leq i \leq M)
• u_i \neq v_i (1 \leq i \leq M)
• If i \neq j, (u_i, v_i) \neq (u_j, v_j).
• 1 \leq S, T \leq N
• S \neq T

Input

Input is given from Standard Input in the following format:

N M u_1 v_1 : u_M v_M S T

Output

If Ken cannot reach Vertex T from Vertex S by repeating ken-ken-pa, print -1. If he can, print the minimum number of ken-ken-pa needed to reach vertex T.

Examples

Input

4 4 1 2 2 3 3 4 4 1 1 3

Output

2

Input

3 3 1 2 2 3 3 1 1 2

Output

-1

Input

2 0 1 2

Output

-1

Input

6 8 1 2 2 3 3 4 4 5 5 1 1 4 1 5 4 6 1 6

Output

2

inputFormat

Input

Input is given from Standard Input in the following format:

N M u_1 v_1 : u_M v_M S T

outputFormat

Output

If Ken cannot reach Vertex T from Vertex S by repeating ken-ken-pa, print -1. If he can, print the minimum number of ken-ken-pa needed to reach vertex T.

Examples

Input

4 4 1 2 2 3 3 4 4 1 1 3

Output

2

Input

3 3 1 2 2 3 3 1 1 2

Output

-1

Input

2 0 1 2

Output

-1

Input

6 8 1 2 2 3 3 4 4 5 5 1 1 4 1 5 4 6 1 6

Output

2

样例

4 4
1 2
2 3
3 4
4 1
1 3

2