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 sys
input = sys.stdin.readline

n,m=map(int,input().split())
EDGE=[tuple(map(int,input().split())) for i in range(m)]

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

# Kahnのアルゴリズム

EDGEIN=[0]*(n+1)# その点に入るEDGEの個数
EDGEOUTLIST=[[] for i in range(n+1)]# EDGEの行き先
for x,y in EDGE:
    EDGEIN[y]+=1
    EDGEOUTLIST[x].append(y)

from collections import deque
QUE = deque()

for i in range(1,n+1):
    if EDGEIN[i]==0:
        QUE.append(i)# 行き先のない点をQUEに入れる



TOP_SORT=[]
while QUE:
    x=QUE.pop()
    TOP_SORT.append(x)# 行き先がない点を答えに入れる
    for to in EDGEOUTLIST[x]:
        EDGEIN[to]-=1# 行き先がない点を削除し,そこから一歩先の点のEDGEINを一つ減らす.
        if EDGEIN[to]==0:
            QUE.appendleft(to)

if len(TOP_SORT)==n:
    print(1)
    print(*[1]*m)

else:
    print(2)
    for x,y in EDGE:
        if x>y:
            print(1,end=" ")
        else:
            print(2,end=" ")