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:
from collections import defaultdict, deque

N, M = map(int, input().split())
G = defaultdict(list)
V = defaultdict(int)

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

q = deque(v for v in range(N) if V[v] == 0)

dp = [0]*(N)
while q:
    From = q.popleft()
    for to in G[From]:
        dp[to] = max(dp[From]+1, dp[to])
        V[to] -= 1
        if V[to] == 0:
            q.append(to)
print(max(dp))