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:
n, m = [int(i) for i in input().split()]
data = []
chil = []
for i in range(n+1):
    chil.append(set())
for j in range(m):
    data.append([int(i) for i in input().split()])
    chil[data[-1][0]].add(data[-1][1])

# done = set()
# fnd = set()
# cycle = False
# def dfs(a):
#     for c in chil[a]:
#         print(a,c)
#         if c in fnd:
#             global cycle
#             cycle = True
#             return
#         if c not in done:
#             fnd.add(c)
#             dfs(c)
# for i in range(1, n+1):
#     if i not in done:
#         dfs(i)
#         done |= fnd
#         fnd = set()
#         if cycle:
#             break

def cycle():
    for i in range(1, n+1):
        stack = [i]
        fnd = [0] * (n+1)
        while stack:
            s = stack.pop()
            for c in chil[s]:
                if c == i:
                    return True
                if not fnd[c]:
                    stack.append(c)
                    fnd[c] = 1





if not cycle():
    print(1)
    l = ['1' for i in range(m)]
    print(' '.join(l))
else:
    print(2)
    for d in data:
        print(["2","1"][d[0] < d[1]], end=' ')
    print()