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>
const long long MOD = 1e9 + 7;
using namespace std;
map<pair<int, int>, int> mp;
vector<long long> adj[5001];
long long ct = 0;
long long col[5001];
long long vis[5001];
void dfs(long long v) {
  vis[v] = 1;
  for (auto u : adj[v]) {
    long long child = u;
    if (vis[child] == 1) {
      mp[{v, child}] = 2;
      ct++;
    } else if (!vis[child])
      dfs(u);
  }
  vis[v] = 2;
}
int main() {
  long long n, m;
  cin >> n >> m;
  long long u, v;
  vector<pair<long long, long long> > vp;
  for (long long i = 0; i < m; i++) {
    cin >> u >> v;
    u -= 1;
    v -= 1;
    mp[{u, v}] = 1;
    vp.push_back({u, v});
    adj[u].push_back(v);
  }
  for (int i = 0; i < n; i++)
    if (!vis[i]) dfs(i);
  cout << (ct ? 2 : 1) << endl;
  for (auto &i : vp) {
    cout << mp[i] << " ";
  }
}