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 = 5005;
int n, m;
vector<int> G[N];
int vis[N], col[N];
int h[N], cnt;
struct Edge {
  int u, v, nxt;
} e[N];
inline void add(int u, int v) {
  e[++cnt] = Edge{u, v, h[u]};
  h[u] = cnt;
}
int fp;
void dfs(int u) {
  vis[u] = 1;
  for (int i = h[u]; i; i = e[i].nxt) {
    int v = e[i].v;
    if (!vis[v])
      dfs(v);
    else if (vis[v] == 1) {
      col[i] = 2;
      fp = 2;
    }
  }
  vis[u] = 2;
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cin >> n >> m;
  for (int i = 1; i <= m; i++) {
    int u, v;
    cin >> u >> v;
    add(u, v);
    col[i] = 1;
  }
  fp = 1;
  for (int i = 1; i <= n; i++)
    if (!vis[i]) dfs(i);
  cout << fp << '\n';
  for (int i = 1; i <= m; i++) cout << col[i] << ' ';
}