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;
vector<int> g[N];
int used[N];
map<pair<int, int>, int> col;
int cl = 1;
void dfs(int v) {
  used[v] = 1;
  for (auto u : g[v]) {
    if (used[u] == 1) {
      col[{v, u}] = 2;
      cl = 2;
    } else {
      col[{v, u}] = 1;
      if (used[u] != 2) dfs(u);
    }
  }
  used[v] = 2;
}
signed main() {
  int n, m;
  cin >> n >> m;
  vector<pair<int, int>> ed;
  for (int i = 0; i < m; ++i) {
    int u, v;
    cin >> u >> v;
    ed.push_back({u, v});
    g[u].push_back(v);
  }
  for (int i = 1; i <= n; ++i)
    if (!used[i]) dfs(i);
  cout << cl << '\n';
  for (auto u : ed) cout << col[{u.first, u.second}] << ' ';
}