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 = 5000 + 3;
vector<pair<int, int>> adj[N];
int n, m, mark[N], c[N], par[N];
bool check;
void input() {
  cin >> n >> m;
  for (int i = 0; i < m; i++) {
    int u, v;
    cin >> u >> v;
    --u, --v;
    adj[u].push_back({v, i});
  }
}
void dfs(int u) {
  mark[u] = 1;
  for (auto [v, id] : adj[u]) {
    if (mark[v] == 0) dfs(v);
    if (mark[v] == 1) c[id] = 1, check = true;
  }
  mark[u] = 2;
}
void output() {
  for (int i = 0; i < n; i++)
    if (mark[i] == 0) dfs(i);
  cout << (check ? 2 : 1) << endl;
  for (int i = 0; i < m; i++) cout << c[i] + 1 << ' ';
  cout << endl;
}
int main() {
  ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  input();
  dfs(0);
  output();
  return 0;
}