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 sys import stdin
input = stdin.readline

n, m = [int(i) for i in input().split()]

edges = [[[0 for i in range(n)], 0] for i in range(n+1)]
edges_2 = [[0, 0] for i in range(m)]

for i in range(m):
    v, w = [int(i) for i in input().split()]
    edges[v][0][edges[v][1]] = w
    edges[v][1] += 1
    edges_2[i] = [v, w]
    
is_one = True
    
for i in range(1, n+1):
    visited = [0 for i in range(n)]
    visited[0] = i
    num_visited = 1
    act = 0
    
    while act <= (num_visited-1):
        for j in range(edges[visited[act]][1]):
            if edges[visited[act]][0][j] == i: is_one = False
            else:
                if edges[visited[act]][0][j] not in visited:
                    visited[num_visited] = edges[visited[act]][0][j]
                    num_visited += 1
        
        act += 1

if is_one:
    print(1)
    for i in range(m-1):
        print("1", end = " ")
    print(1)
    
else:
    print(2)
    for i in range(m-1):
        if edges_2[i][0] < edges_2[i][1]: print("1", end = " ")
        else: print("2", end = " ")
    if edges_2[-1][0] < edges_2[-1][1]: print("1")
    else: print("2")