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:
v_n, e_n = tuple(map(int, input().split()))
G = [set() for _ in range(v_n)]
edges = []
d_s = [-1] * v_n
ok = False
def dfs(u):
    global ok
    if ok:
        return
    d_s[u] = 0
    for v in G[u]:
        if d_s[v] == -1:
            dfs(v)
        elif d_s[v] == 0:
            ok = True
    d_s[u] = 1

for _ in range(e_n):
    u, v = tuple(map(int, input().split()))
    u -= 1
    v -= 1
    edges.append((u, v))
    G[u].add(v)


for u in range(v_n):
    if d_s[u]==-1:
        dfs(u)


if not ok:
    print(1)
    for _ in range(e_n):
        print(1, end=' ')
else:
    print(2)
    for (u, v) in edges:
        print(int(u < v) + 1, end=' ')