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:
from collections import defaultdict
vis=[]
def isCyclic(n, graph):
    global vis
    global k
    vis=[0]*n
    rec=[0]*n
    for i in range(0,n):
        if(vis[i]== False):
            if(DfsRec(i,rec,graph)):
                #print("ss")
                j=0
    return False

def DfsRec(i,rec,g):
    global s1
    global s2
    global vis
    global k
    vis[i]=True
    rec[i]=True
    for u in g[i]:
 #       print(u,rec,g)
        if(vis[u]==False):
            DfsRec(u,rec,g)
        elif(rec[u]==True):
            k=1
            colors[(i,u)]=2
            s1=i
            s2=u
    rec[i]=False
    return False

n,e=list(map(int,input().split()))
d=defaultdict(lambda:[])
colors=defaultdict(lambda:1)
l=[]
for i in range(0,e):
    a,b=list(map(int,input().split()))
    l.append([a-1,b-1])
    d[a-1].append(b-1)
#print(d)
s1=-1
s2=-1
k=0
c=isCyclic(n,d)
#print(k)
#print(s1,s2)
#print(colors)
if(k==1):
    print(2)
    ans=[]
    for i,j in l:
        ans.append(colors[(i,j)])
    print(*ans)
else:
    print(1)
    l=[1]*e
    print(*l)