Coloring Edges CodeForces - 1217D

You are given a directed graph with $n$

Let's denote the $k$

Find a good $k$

Input

The first line contains two integers $n$

Next $m$

It is guaranteed that each ordered pair $(u, v)$

Output

In the first line print single integer $k$

In the second line print $m$

If there are multiple answers print any of them (you still have to minimize $k$

Examples

Input

Output

1
1 1 1 1 1

Input

Output

2
1 1 2

#include<bits/stdc++.h>//网上大佬的代码 
using namespace std;
typedef long long ll;
const int maxn = 5e3+5;
const int inf = 0x3f3f3f3f;
int n, m, d[maxn], res[maxn];

vector<int> g[maxn];

struct node {
    int u, v;
    node(int u = 0, int v = 0) : u(u), v(v) {}
}edge[maxn];

int topo()//拓扑排序 
{
    int cnt = 0;
    
    queue<int> q;
    for (int i = 1; i <= n; i++)
        if (d[i] == 0) q.push(i);
        
    while (!q.empty()) {
        int t = q.front(); q.pop();
        cnt++; 
        for (int i = 0; i < g[t].size(); i++) {
            int v = g[t][i];
            d[v]--;
            if (d[v] == 0)
                q.push(v);
        }
    }
    if (cnt == n)
        return 1;
    return 0;
}

int main()
{
    cin >> n >> m;
    memset(d, 0, sizeof(d));
    
    for (int i = 0; i < m; i++) {
        int u, v;
        cin >> u >> v;
        if (u > v)
            res[i] = 2;
        else
            res[i] = 1;
            
        g[u].push_back(v);//记录u指向v; 
        
        d[v]++;
    }
    
    if (topo()) 
    {
        cout << 1 << "\n";
        for (int i = 0; i < m; i++)
            printf("1 ");
        cout << "\n";
        
    } else {
        
        cout << 2 << "\n";
        for (int i = 0; i < m; i++)
            printf("%d ", res[i]);
        cout << "\n";
    }
    return 0;
}

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 $m$ ( $2 \leq n \leq 5000$ , $1 \leq m \leq 5000$ ) — 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 $v$ ( $1 \leq u, v \leq n$ , $u \neq v$ ) — 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 $c_{1}, c_{2}, \dots, c_{m}$ ( $1 \leq c_{i} \leq k$ ), 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

Output

1
1 1 1 1 1

Input

Output

2
1 1 2

来源：https://www.cnblogs.com/qqshiacm/p/11656827.html

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