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 os
import sys
from collections import defaultdict


def get_adj(edges):
    neighbors = defaultdict(list, {})
    for v1, v2 in edges:
        neighbors[v1].append(v2)

    return dict(neighbors)


NEW = 0
VISITING = 1
CLOSED = 2

def solve(edges, n):
    adj = get_adj(edges)
    status = [NEW] * (n + 1)

    edge_idx = {tuple(e): idx for idx, e in enumerate(edges)}
    colors = [1] * len(edges)

    has_loop = [False]

    def dfs(root):
        if status[root] == CLOSED:
            return

        status[root] = VISITING

        children = adj.get(root, [])
        for c in children:
            if status[c] == NEW:
                dfs(c)
            elif status[c] == VISITING:
                colors[edge_idx[(root, c)]] = 2
                has_loop[0] = True
            elif status[c] == CLOSED:
                pass

        status[root] = CLOSED

    for i in range(1, n + 1):
        dfs(i)

    return has_loop[0], colors


def pp(input):
    n, m = map(int, input().strip().split())
    edges = [tuple(map(int, input().strip().split())) for _ in range(m)]
    has_loop, colors = solve(edges, n)
    print(int(has_loop) + 1)
    print(" ".join(map(str, colors)))


if "pydev" in sys.argv[0]:
    from string_source import string_source, codeforces_parse
    x = """inputCopy
4 5
1 2
1 3
3 4
2 4
1 4
outputCopy
1
1 1 1 1 1 
inputCopy
3 3
1 2
2 3
3 1
outputCopy
2
1 1 2 """

    for q, a in codeforces_parse(x):
        pp(string_source(q))
        print(a)
        print("----")
else:
    pp(sys.stdin.readline)