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;

const int N = 1e5 + 10;

vector<int> v[N];
int f[N];
int DP(int x) {
    int &ans = f[x];
    if (ans != -1) return ans;
    ans = 0;
    for(auto y : v[x]) ans = max(ans, DP(y) + 1);
    return ans;
}
int main() {
    int n, m;
    cin >> n >> m;
    while (m--) {
        int x, y;
        cin >> x >> y;
        v[x].push_back(y);
    }
    memset(f, -1, sizeof(f));
    int ans = 0;
    for(int i = 1; i <= n; i++) ans = max(ans, DP(i));
    cout << ans;
}