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:
WHITE, GRAY, BLACK = 0, 1, 2


def solve(graph: [], colors: []):
    n = len(graph)-1
    visited = [WHITE] * (n + 1)
    returnValue = 1
    for i in range(1, n + 1):
        if visited[i] == WHITE and Dfs(graph, colors, i, visited):
            returnValue = 2
    return returnValue


def Dfs(graph: [], colors: [], id, visited: []):
    visited[id] = GRAY
    returnValue = False
    for adj, colorId in graph[id]:
        if visited[adj] == WHITE:
            val = Dfs(graph, colors, adj, visited)
            returnValue=True if val else returnValue
        elif visited[adj] == GRAY:
            returnValue = True
            colors[colorId] = 2
    visited[id] = BLACK
    return returnValue


n, m = [int(x) for x in input().split()]
graph = [[] for _ in range(n + 1)]
colors = [1] * (m)
for i in range(m):
    u, v = [int(x) for x in input().split()]
    graph[u].append((v, i))
print(solve(graph,colors))
for color in colors:
    print(color,end=" ")
print()