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:
def dfs(inp, stat, u):
    if stat[u] > 1:
        return stat[u] < 3
    stat[u] = 2
    for v in inp[u]:
        if dfs(inp, stat, v):
            return True
    stat[u] = 3
    return False


def main():
    ans = []
    n, m = map(int, input().split())
    inp = tuple(([] for _ in range(n + 1)))
    for _ in range(m):
        u, v = map(int, input().split())
        ans.append((u > v) + 1)
        inp[u].append(v)
    stat = [1] * (n + 1)
    for u in range(n + 1):
        if dfs(inp, stat, u):
            print(2)
            print(*ans)
            break
    else:
        print(1)
        print(*(1,) * m)


main()