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 = input().split(' ')
n, m = int(n), int(m)

ch = [[] for i in range(n+1)]

edges_by_order = []

for i in range(m):
    x, y = input().split(' ')
    x, y = int(x), int(y)
    ch[x].append(y)
    edges_by_order.append((x, y))

for i in range(n+1):
    ch[i] = sorted(ch[i])

st = [0 for i in range(n+1)]
end = [0 for i in range(n+1)]

timestamp = 0
cycle_exists = False

def dfs(x):
    global ch, st, end, timestamp, cycle_exists
    
    timestamp += 1
    st[x] = timestamp
    
    for y in ch[x]:
        if st[y] == 0:
            dfs(y)
        else:
            if st[y] < st[x] and end[y] == 0:
                cycle_exists = True
    
    timestamp += 1
    end[x] = timestamp

for i in range(1, n+1):
    if st[i] == 0:
        dfs(i)

if not cycle_exists:
    print(1)
    for i in range(m):
        print(1, end=' ')
    print('', end='\n')
else:
    print(2)
    for i in range(m):
        x = st[edges_by_order[i][0]]
        y = st[edges_by_order[i][1]]
        
        if x < y:
            print(1, end=' ')
        else:
            print(2, end=' ')
    print('', end='\n')