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:
class Graph:
    def __init__(self, n, m):
        self.nodes = n
        self.edges = m
        self.adj = [[] for i in range(n)]
        self.color = [1 for i in range(m)]
        self.vis = [0 for i in range(n)]
        self.colors = 1

    def add_edge(self, u, v, i):
        self.adj[u].append((i, v))

    def dfs(self, u):
        self.vis[u] = 1
        for i, v in self.adj[u]:
            if self.vis[v] == 1:
                self.colors = 2
                self.color[i] = 2
            if self.vis[v] == 0:
                self.dfs(v)
        self.vis[u] = 2

    def solve(self):
        for i in range(self.nodes):
            if self.vis[i] == 0:
                self.dfs(i)
        print(self.colors)
        print(' '.join(map(str, self.color)))


n, m = map(int, input().split(' '))
graph = Graph(n, m)
for i in range(m):
    u, v = map(int, input().split(' '))
    graph.add_edge(u-1, v-1, i)
graph.solve()