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<int> status, ans;
vector<vector<pair<int, int>>> graph;
void dfs(int node) {
  status[node] = 1;
  for (auto x : graph[node]) {
    if (status[x.first] == 1) {
      ans[x.second] = 2;
    } else {
      ans[x.second] = 1;
      if (status[x.first] == 0) dfs(x.first);
    }
  }
  status[node] = 2;
}
int main() {
  int nodeCount, edgeCount;
  cin >> nodeCount >> edgeCount;
  graph = vector<vector<pair<int, int>>>(nodeCount + 1);
  ans = vector<int>(edgeCount, 0);
  status = vector<int>(nodeCount + 1, 0);
  int from, to;
  for (int i = 0; i < edgeCount; i++) {
    cin >> from >> to;
    graph[from].push_back({to, i});
  }
  for (int i = 1; i <= nodeCount; i++) {
    if (status[i] == 0) {
      dfs(i);
    }
  }
  cout << *max_element(ans.begin(), ans.end()) << endl;
  for (int i = 0; i < edgeCount; i++) cout << ans[i] << " ";
  cout << endl;
}