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(10000)

def solve(g):
    dp = [-1]*len(g)
    def _solve(f):
        if dp[f] == -1:
            dp[f] = 0
            for c in g[f]:
                dp[f] = max(dp[f], 1 + _solve(c))
        return dp[f]
    for f in range(len(g)):
        _solve(f)
    # print(dp)
    return max(dp)

n, m = map(int, input().split())
g = [[] for _ in range(n)]
for _ in range(m):
    f, t = map(int, input().split())
    g[f-1].append(t-1)

print(solve(g))