Keshi in Search of AmShZ

Description:

Input:

The first line of the input contains two integers $$$n$$$ and $$$m$$$ $$$(2 \le n \le 2 \cdot 10^5, 1 \le m \le 2 \cdot 10^5)$$$  — the number of cities and roads correspondingly.

The $$$i$$$-th line of the following $$$m$$$ lines contains two integers $$$v_i$$$ and $$$u_i$$$ $$$(1 \le v_i , u_i \le n,v_i \neq u_i)$$$, denoting a directed road going from city $$$v_i$$$ to city $$$u_i$$$.

It is guaranteed that there is at least one route from city $$$1$$$ to city $$$n$$$. Note that there may be more than one road between a pair of cities in each direction.

Output:

Output the smallest possible integer $$$d$$$ to make sure that AmShZ and Keshi will see each other after at most $$$d$$$ days.

Sample Input:

2 1
1 2

Sample Output:

1

Sample Input:

4 4
1 2
1 4
2 4
1 4

Sample Output:

2

Sample Input:

5 7
1 2
2 3
3 5
1 4
4 3
4 5
3 1

Sample Output:

4

Note:

In the first sample, it's enough for AmShZ to send the second type of message.

In the second sample, on the first day, AmShZ blocks the first road. So the only reachable city from city $$$1$$$ will be city $$$4$$$. Hence on the second day, AmShZ can tell Keshi to move and Keshi will arrive at AmShZ's house.

It's also possible for AmShZ to tell Keshi to move for two days.