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:
'''
  Author: Ashraful Islam Fuad
  University of Asia Pacific
  Bsc in CSE
  category:DFS (dificulty 2000)
  problem :from codeforces 
sd
'''
from collections  import defaultdict

ans=defaultdict(lambda :1)

flag=0


def dfs(node):
	global flag
	visit[node]=1


	for j in graph[node]:
		if not visit[j]:
			dfs(j)

		else:
			if visit[j]==1:
				flag=1
				ans[(node,j)]=2

	visit[node]=2


n,m=map(int,input().split())

graph=defaultdict(list)


parent=[0]+[i+1 for i in range(n)]


for i in range(m):
	e1,e2=map(int,input().split())
	graph[e1].append(e2)

	ans[(e1,e2)]=1


visit=[0]*(n+1)


for i in range(n):

	if visit[i]==0:
		dfs(i)




if flag:
	print(2)
else:
	print(1)

for i in ans:
	# print('i is {}'.format(i))  
	print(ans[i],end=' ')