Problem: There is a directed graph G with N vertices and M edges. The vertices are numbered 1, 2, \ldots, N, and for each i (1 \leq i \leq M), the i-th directed edge goes from Vertex x_i to y_i. G does not contain directed cycles.

Find the length of the longest directed path in G. Here, the length of a directed path is the number of edges in it.

Constraints

* All values in input are integers.
* 2 \leq N \leq 10^5
* 1 \leq M \leq 10^5
* 1 \leq x_i, y_i \leq N
* All pairs (x_i, y_i) are distinct.
* G does not contain directed cycles.

Input

Input is given from Standard Input in the following format:


N M
x_1 y_1
x_2 y_2
:
x_M y_M


Output

Print the length of the longest directed path in G.

Examples

Input

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


Output

3


Input

6 3
2 3
4 5
5 6


Output

2


Input

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


Output

3

Solution (in PYTHON3):

Solution:
import sys
sys.setrecursionlimit(1000000)


N, M = map(int, input().split())

G = {k: [] for k in range(N)}
for _ in range(M):
    x, y = map(int, input().split())

    # 有向グラフ
    G[x-1].append(y-1)  # 0-indexed

dp = [-1 for _ in range(100100)]


def rec(v):
    if dp[v] != -1:
        return dp[v]

    dp[v] = 0
    for nv in G[v]:
        dp[v] = max(dp[v], rec(nv)+1)

    return dp[v]


ans = 0
for v in range(N):
    ans = max(ans, rec(v))
print(ans)