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 PYTHON):

Solution:
from collections import Counter, deque, defaultdict as ddic
from itertools import combinations, permutations, product

GRAY, BLACK = 0, 1

def topological(graph):
    ans, enter, state = [], set(graph), {}
    terrible = [False]
    def dfs(node):
        state[node] = GRAY
        for k in graph.get(node, ()):
            sk = state.get(k, None)
            if sk == GRAY:
                terrible[0] = True
                continue
            if sk == BLACK: continue
            enter.discard(k)
            dfs(k)
        ans.append(node)
        state[node] = BLACK

    while enter: dfs(enter.pop())
    return ans[::-1], terrible[0]
    
rr = raw_input
rri = lambda: int(raw_input())
rrm = lambda: map(int, raw_input().split())
MOD = 10**9 + 7
YES, NO = "Yes", "No"

def solve(N, M, edges):
    graph = ddic(list)
    for u, v in edges:
        graph[u].append(v)

    T,terrib = topological(graph)
    Ti = {v: i for i,v  in enumerate(T)}
    colors = [1] * M
    ans = 1
    if terrib: ans = 2
    for i, edge in enumerate(edges):
        if Ti[edge[0]] > Ti[edge[1]]:
            colors[i] = 2
            ans = 2
    return ans, colors


N, M = rrm()
edges = []
for _ in xrange(M):
    u, v = rrm()
    edges.append((u-1,v-1))

numcolors, row = solve(N, M, edges)
print numcolors
print " ".join(map(str, row))