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 PYTHON3):

Solution:
import math
# import sys
# input = sys.stdin.readline
n,m=[int(i) for i in input().split(' ')]
d=[[] for i in range(n)]
done = [False for i in range(n)]
def dfs(visited,i,d):
    visited[i]=True
    done[i] = True
    for j in d[i]:
        if visited[j]:
            return True
        if not done[j]:
            temp = dfs(visited,j,d)
            if temp:return True
    visited[i]=False
    return False
edgelist=[]
for i in range(m):
    a,b=[int(i) for i in input().split(' ')]
    edgelist.append([a,b])
    d[a-1].append(b-1)

ans = 0
visited=[False for i in range(n)]
for i in range(n):
    if dfs(visited,i,d):
        ans = 1
        break
if ans:
    print(2)
    for i in edgelist:
        if i[0]>i[1]:
            print(2,end=' ')
        else:print(1,end=' ')
else:
    print(1)
    print(' '.join('1' for i in range(m)))