Problem:
Score : 100 points

Problem Statement

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.

Sample Input 1

4 5
1 2
1 3
3 2
2 4
3 4

Sample Output 1

3

The red directed path in the following figure is the longest:

Sample Input 2

6 3
2 3
4 5
5 6

Sample Output 2

2

The red directed path in the following figure is the longest:

Sample Input 3

5 8
5 3
2 3
2 4
5 2
5 1
1 4
4 3
1 3

Sample Output 3

3

The red directed path in the following figure is one of the longest:

Solution in C++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <vector>

long max_vec(std::vector<long> dp) {
    long max = 0;
    for(int i = 0; i < dp.size(); ++i) {
        if(max < dp[i]) {
            max = dp[i];
        }
    }
    return max;
}

int main() {
    int N, M;
    std::cin >> N >> M;
    std::vector<long> dp(N, 0);
    for(int k = 0; k < M; ++k) {
        int i, j;
        std::cin >> i >> j;
        dp[j-1] = std::max(dp[j-1], 1 + dp[i-1]);
    }
    std::cout << max_vec(dp) << "\n";
    return 0;
}