Problem: You are given a directed graph with n vertices and m directed edges without self-loops or multiple edges.

Let's denote the k-coloring of a digraph as following: you color each edge in one of k colors. The k-coloring is good if and only if there no cycle formed by edges of same color.

Find a good k-coloring of given digraph with minimum possible k.

Input

The first line contains two integers n and m (2 ≤ n ≤ 5000, 1 ≤ m ≤ 5000) — the number of vertices and edges in the digraph, respectively.

Next m lines contain description of edges — one per line. Each edge is a pair of integers u and v (1 ≤ u, v ≤ n, u ≠ v) — there is directed edge from u to v in the graph.

It is guaranteed that each ordered pair (u, v) appears in the list of edges at most once.

Output

In the first line print single integer k — the number of used colors in a good k-coloring of given graph.

In the second line print m integers c_1, c_2, ..., c_m (1 ≤ c_i ≤ k), where c_i is a color of the i-th edge (in order as they are given in the input).

If there are multiple answers print any of them (you still have to minimize k).

Examples

Input


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


Output


1
1 1 1 1 1 


Input


3 3
1 2
2 3
3 1


Output


2
1 1 2 

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int N = 5001;
int ans[N], color[N];
vector<pair<long long, long long> > g[N];
bool fin = false;
void dfs(int v) {
  color[v] = 1;
  for (auto it : g[v]) {
    int to = it.first, idx = it.second;
    if (color[to] == 0) {
      dfs(to);
      ans[idx] = 1;
    } else if (color[to] == 2) {
      ans[idx] = 1;
    } else {
      ans[idx] = 2;
      fin = true;
    }
  }
  color[v] = 2;
}
int main() {
  int n;
  cin >> n;
  int m;
  cin >> m;
  int x, y, c = 1;
  while (m--) {
    cin >> x >> y;
    g[x].push_back({y, c++});
  }
  m = --c;
  for (int i = 1; i <= n; i++)
    if (!color[i]) dfs(i);
  cout << fin + 1 << "\n";
  for (int i = 1; i <= m; i++) {
    cout << ans[i] << " ";
  }
}