There is a simple directed graph with $N$ vertices numbered from $1$ to $N$ and $M$ edges. The $i$-th edge $(1 \leq i \leq M)$ is a directed edge from vertex $a_i$ to vertex $b_i$.
Determine whether there exists a cycle that contains vertex $1$, and if it exists, find the minimum number of edges among such cycles.

The input is given from Standard Input in the following format:

$N$ $M$

$a_1$ $b_1$

$a_2$ $b_2$

$\vdots$

$a_M$ $b_M$

If there exists a cycle that contains vertex $1$, print the minimum number of edges among such cycles. Otherwise, print -1.

• $2 \leq N \leq 2 \times 10^5$
• $1 \leq M \leq \min \left( \frac{N(N-1)}{2},\ 2 \times 10^5 \right)$
• $1 \leq a_i \leq N$
• $1 \leq b_i \leq N$
• $a_i \neq b_i$
• $(a_i, b_i) \neq (a_j, b_j)$ and $(a_i, b_i) \neq (b_j, a_j)$, if $i \neq j$.
• All input values are integers.

Vertex $1$ $\to$ vertex $2$ $\to$ vertex $3$ $\to$ vertex $1$ is a cycle with three edges, and this is the only cycle that contains vertex $1$.