Problem Description

As we know, Rikka is poor at math. Yuta is worrying about this situation, so he gives Rikka some math tasks to practice. There is one of them:

Yuta has a non-direct graph with n vertices and m
edges. The length of each edge is 1. Now he wants to add exactly an
edge which connects two different vertices and minimize the length of
the shortest path between vertice 1 and vertice n. Now he wants to know the minimal length of the shortest path and the number of the ways of adding this edge.

It is too difficult for Rikka. Can you help her?

 

Input

There are no more than 100 testcases.

For each testcase, the first line contains two numbers n,m(2≤n≤100,0≤m≤100).

Then m lines follow. Each line contains two numbers u,v(1≤u,v≤n) , which means there is an edge between u and v. There may be multiedges and self loops.

 

Output

For each testcase, print a single line contains two numbers: The length of the shortest path between vertice 1 and vertice n and the number of the ways of adding this edge.

 

Sample Input

 

Sample Output

1 1

#include <iostream>

#include <cstdio>

#include <cstring>

#include <cmath>

#include <algorithm>

#include <set>

#include <queue>

#include <vector>

#define LL long long

using namespace std;

int n, m;

bool dis[][];

int input()

{

    if (scanf("%d%d", &n, &m) == EOF)

        return false;

    memset(dis, false, sizeof(dis));

    int u, v;

    for (int i = ; i < m; ++i)

    {

        scanf("%d%d", &u, &v);

        dis[u][v] = dis[v][u] = true;

    }

    return true;

}

void work()

{

    printf("1 ");

    if (dis[][n])

        printf("%d\n", n*(n-)/);

    else

        printf("1\n");

}

int main()

{

    //freopen("test.in", "r", stdin);

    while (input())

    {

        work();

    }

    return ;

}