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>
int read() {
  register int x = 0;
  register char ch = getchar(), f = 1;
  for (; !isdigit(ch); ch = getchar())
    if (ch == '-') f = !f;
  for (; isdigit(ch); ch = getchar()) x = (x << 1) + (x << 3) + (ch ^ '0');
  return f ? x : -x;
}
int n, m, ans, vis[5005];
int edge, to[5005], pr[5005], hd[5005], col[5005];
void addedge(int u, int v) { to[++edge] = v, pr[edge] = hd[u], hd[u] = edge; }
void dfs(int u) {
  vis[u] = 2;
  for (register int i = hd[u], v; i; i = pr[i])
    if (!col[i]) {
      v = to[i];
      if (!vis[v]) dfs(v);
      if (vis[v] == 2)
        col[i] = 2, ans = 2;
      else
        col[i] = 1;
    }
  vis[u] = 1;
}
int main() {
  n = read(), m = read();
  for (register int i = 1, u, v; i <= m; ++i)
    u = read(), v = read(), addedge(u, v);
  ans = 1;
  for (register int i = 1; i <= n; ++i)
    if (!vis[i]) dfs(i);
  printf("%d\n", ans);
  for (register int i = 1; i <= m; ++i) printf("%d ", col[i]);
}