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:
n, m = map(int, input().split())
g_o = [[] for x in range(n)]
g_i = [0] * n
for _ in range(m):
    p, c = map(int, input().split())
    g_o[p - 1].append(c - 1)
    g_i[c - 1] += 1
sor = [e for e in range(n) if g_i[e] == 0]
for node in sor:
    for i in g_o[node]:
        g_i[i] -= 1
        if g_i[i] == 0:
            sor.append(i)
dp = [0] * n
for node in sor:
    for c in g_o[node]:
        if dp[c] < dp[node] + 1:
            dp[c] = dp[node] + 1
print(max(dp))