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
# 許容する再帰処理の回数を変更
sys.setrecursionlimit(10**5+10)
# input処理を高速化する


N,M = map(int,input().split())
to = [[] for i in range(N)]
for i in range(M):
    x,y = map(int,input().split())
    to[x-1]+=[y-1]

dp = [-1 for i in range(N)] #node[i]からの最長経路長を記す -1で未決定を示す

def memo(i):
    if dp[i] != -1:
        return dp[i]
    a=0
    for j in to[i]:
        a=max(a, memo(j)+1)
    dp[i] = a
    return a

lp = 0
for i in range(N):
    lp = max(lp,memo(i))
print(lp)