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:
n,m=map(int,input().split())
L=[]
for i in range(n):
    s=[]
    L.append(s)

st=[]
for i in range(m):
    u,v=map(int,input().split())
    st.append((u-1,v-1))
    L[u-1].append(v-1)

visited=[False]*n
rs=[False]*n

def dfs(u):
    if(visited[u]==False):
        visited[u]=True
        rs[u]=True
        for i in L[u]:
            if(visited[i]==False and dfs(i)==True):
                return True
            elif(rs[i]==True):
                return True

    rs[u]=False
    return False


flag=0
for i in range(0,n):
    if(dfs(i)==True):
        flag=1
        break


if(flag==0):
    print(1)
    for i in range(m):
        print(1,end=" ")
    print(" ")

else:
    print(2)
    for i in range(0,len(st)):
        if(st[i][0]<st[i][1]):
            print(1,end=" ")
        else:
            print(2,end=" ")
    print(" ")