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 = 2e5 + 5;
int n, m, t, h[N], nx[N], e[N];
void Add(int x, int y) {
  nx[++t] = h[x];
  e[h[x] = t] = y;
}
vector<int> u[N];
int dg[N], a[N];
bool f[N];
void Dfs(int x) {
  if (f[x]) return;
  f[x] = 1;
  for (int i = h[x]; i; i = nx[i]) {
    a[i] = (x < e[i]);
    Dfs(e[i]);
  }
}
void Topo() {
  queue<int> q;
  for (int i = 1; i <= n; i++) {
    if (!dg[i]) q.push(i);
  }
  while (!q.empty()) {
    int x = q.front();
    q.pop();
    for (auto K : u[x]) {
      if (!(--dg[K])) q.push(K);
    }
  }
  bool uu = 0;
  for (int i = 1; i <= n; i++)
    if (dg[i]) uu = 1;
  if (!uu) {
    puts("1");
    for (int i = 1; i <= t; i++) printf("1 ");
    return;
  }
  for (int i = 1; i <= n; i++)
    if (dg[i] && !f[i]) Dfs(i);
  puts("2");
  for (int i = 1; i <= t; i++) printf("%d ", a[i] + 1);
}
int main() {
  scanf("%d%d", &n, &m);
  for (int x, y; m--;) {
    scanf("%d%d", &x, &y);
    u[x].push_back(y);
    dg[y]++;
    Add(x, y);
  }
  Topo();
  return 0;
}