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 long long MX = 5010;
map<pair<long long, long long>, long long> tipo;
long long ans[MX];
vector<long long> adj[MX];
long long estado[MX];
long long K = 1;
void dfs(long long u) {
  estado[u] = 1;
  for (long long v : adj[u]) {
    if (estado[v] == 0) {
      dfs(v);
    } else if (estado[v] == 1) {
      tipo[{u, v}]++;
      K = 2;
    }
  }
  estado[u] = 2;
  return;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  cout.precision(10);
  cout << fixed;
  vector<pair<long long, long long> > ari;
  long long n, m, x, y;
  cin >> n >> m;
  for (long long i = 0; i < m; i++) {
    cin >> x >> y;
    adj[x].push_back(y);
    tipo[{x, y}] = 0;
    ari.push_back({x, y});
  }
  for (long long i = 1; i <= n; i++) {
    if (estado[i] == 0) dfs(i);
  }
  cout << K << endl;
  for (long long i = 0; i < m; i++) {
    cout << tipo[ari[i]] + 1 << " ";
  }
  cout << endl;
  return 0;
}