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:
colors = 1
n, m = map(int, input().split(' '))
adj = [[] for i in range(n)]
color = [0 for i in range(m)]
vis = [0 for i in range(n)]


def dfs(u):
    global colors
    vis[u] = 1
    for i, v in adj[u]:
        if vis[v] == 1:
            colors = 2
            color[i] = 2
        else:
            color[i] = 1
            if vis[v] == 0:
                dfs(v)
    vis[u] = 2


for i in range(m):
    u, v = map(int, input().split(' '))
    adj[u-1].append((i, v-1))
for i in range(n):
    if vis[i] == 0:
        dfs(i)
print(colors)
print(' '.join(map(str, color)))