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;
vector<pair<int, int> > adj[5005];
vector<int> intime(5005, 0), outtime(5005, 0), color(5005, 0);
int colcnt = 1, tme = 1;
void dfs(int node) {
  intime[node] = tme++;
  for (auto it : adj[node]) {
    if (intime[it.first] != 0 && outtime[it.first] == 0) {
      colcnt = 2;
      color[it.second] = 1;
    } else if (outtime[it.first] == 0) {
      dfs(it.first);
    }
  }
  outtime[node] = tme++;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  int n, m;
  cin >> n >> m;
  for (int i = 0; i < m; ++i) {
    int x, y;
    cin >> x >> y;
    adj[x].push_back({y, i});
  }
  for (int i = 1; i <= n; ++i)
    if (intime[i] == 0) dfs(i);
  cout << colcnt << "\n";
  for (int i = 0; i < m; ++i) {
    cout << color[i] + 1 << " ";
  }
  return 0;
}