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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;

int n, m;
int dp[100010];
vector<int> g[100010];

int calc(int u) {
    int &y = dp[u];
    if(y != -1) return y;
    y = 0;
    for(auto&v: g[u]) {
        y = max(y, 1+calc(v));
    }
    return y;
}

int main() {
    memset(dp, -1, sizeof(dp));
	cin >> n >> m;
	while(m--) {
	    int x, y;
	    cin >> x >> y;
	    g[x].push_back(y);
	}
	int ans = 0;
	for(int i=1; i<=n; ++i) {
	    ans = max(ans, calc(i));
	}
	cout << ans << endl;
	return 0;
}