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 = int(n)
m = int(m)
ady = [[] for _ in range(n + 1)]
low = [0] * (n + 1)
vdfs = [0] * (n + 1)
ndfs = int(0)
oneColor = True
mark = [False] * (n + 1)
sol = [0] * m

def dfs(nod):
    global sol, ndfs, ady, vdfs, low, oneColor, ant, pila
    ndfs += 1
    vdfs[nod] = low[nod] = ndfs
    for par in ady[nod]:
        to = par[0]
        index = par[1]
        sol[index] = 1
        if(vdfs[to] == 0):
            dfs(to)
            low[nod] = min(low[to], low[nod])
        elif(mark[to] == False):
            low[nod] = min(low[nod], vdfs[to])
            if(low[to] <= vdfs[nod]):
                oneColor = False
                sol[index] = 2
    mark[nod] = True

for i in range(m):
    n1, n2 = input().split()
    n1 = int(n1)
    n2 = int(n2)
    ady[n1].append((n2, i))

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

if(oneColor):
    print(1)
else:
    print(2)

res = str("")
for i in range(0, m):
    res += str(sol[i]) + str(" ")

print(res)