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;
bool f = 0;
vector<int> v[5555];
bool vis[5555];
int a[5555];
void dfs(int x, int s) {
  vis[x] = 1;
  for (int i : v[x]) {
    if (i == s) {
      f = 1;
      return;
    }
    if (!vis[i]) dfs(i, s);
  }
}
int main() {
  int n, m;
  scanf("%d%d", &n, &m);
  for (int i = 0; i < m; i++) {
    int x, y;
    scanf("%d%d", &x, &y);
    if (x < y)
      a[i] = 1;
    else
      a[i] = 2;
    v[x].push_back(y);
  }
  int k = 1;
  for (int i = 1; i <= n; i++) {
    f = 0;
    memset(vis, 0, sizeof(vis));
    dfs(i, i);
    if (f) {
      k = 2;
      break;
    }
  }
  printf("%d\n", k);
  if (k == 1) {
    for (int i = 0; i < m; i++) printf("1 ");
    printf("\n");
  } else {
    for (int i = 0; i < m; i++) printf("%d ", a[i]);
    printf("\n");
  }
}