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:
def iscyclic(s,visited,restack):
    visited[s]=True
    restack[s]=True
    
    if s in adj:
        for u in adj[s]:
            if visited[u]==False:
                if iscyclic(u,visited,restack)==True:
                    return True
            elif restack[u]==True:
                return True
    restack[s]=False
    return False
    
def cyclic():
    visited=[False]*(n+1)
    restack=[False]*(n+1)
    for u in adj:
        if visited[u]==False:
            if iscyclic(u,visited,restack)==True:
                return True
    return False
    
n,m=map(int,input().split())
adj={}
l=[]
for i in range(m):
    a,b=map(int,input().split())
    if a not in adj:
        adj[a]=[b]
    else:
        adj[a].append(b)
    l.append([a,b])
visited=[False]*(n+1)
bo=cyclic()
if bo==False:
    print(1)
    for i in range(m):
        print(1,end=" ")
else:
    print(2)
    for i in range(m):
        if l[i][0]>l[i][1]:
            print(2,end=" ")
        else:
            print(1,end=" ")