A - New Bus Route_a - bus route-优快云博客

本文介绍了一个计算问题，即找出n个城市坐标中具有最小距离的两个城市的距离及具有该距离的城市对数量。通过排序和遍历的方法高效解决了此问题。

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Description

There are n cities situated along the main road of Berland. Cities are represented by their coordinates — integer numbers a₁, a₂, ..., a_n. All coordinates are pairwise distinct.

It is possible to get from one city to another only by bus. But all buses and roads are very old, so the Minister of Transport decided to build a new bus route. The Minister doesn't want to spend large amounts of money — he wants to choose two cities in such a way that the distance between them is minimal possible. The distance between two cities is equal to the absolute value of the difference between their coordinates.

It is possible that there are multiple pairs of cities with minimal possible distance, so the Minister wants to know the quantity of such pairs.

Your task is to write a program that will calculate the minimal possible distance between two pairs of cities and the quantity of pairs which have this distance.

Input

The first line contains one integer number n (2 ≤ n ≤ 2·10⁵).

The second line contains n integer numbers a₁, a₂, ..., a_n ( - 10⁹ ≤ a_i ≤ 10⁹). All numbers a_i are pairwise distinct.

Output

Print two integer numbers — the minimal distance and the quantity of pairs with this distance.

Sample Input

Input

4
6 -3 0 4

Output

2 1

Input

3
-2 0 2

Output

2 2

Description

There are n cities situated along the main road of Berland. Cities are represented by their coordinates — integer numbers a₁, a₂, ..., a_n. All coordinates are pairwise distinct.

It is possible that there are multiple pairs of cities with minimal possible distance, so the Minister wants to know the quantity of such pairs.

Your task is to write a program that will calculate the minimal possible distance between two pairs of cities and the quantity of pairs which have this distance.

Input

The first line contains one integer number n (2 ≤ n ≤ 2·10⁵).

The second line contains n integer numbers a₁, a₂, ..., a_n ( - 10⁹ ≤ a_i ≤ 10⁹). All numbers a_i are pairwise distinct.

Output

Print two integer numbers — the minimal distance and the quantity of pairs with this distance.

Sample Input

Input

4
6 -3 0 4

Output

2 1

Input

3
-2 0 2

Output

2 2

题意：

找差最小的数，看有多少个这样的

分析：

就是先排序，做差，然后找最小的判断有多少个

代码：

#include<bits/stdc++.h>
using namespace std;
int main()
{
    long int a[200005],b[200005],i,n,s=1;
    cin>>n;
    for(i=0;i<n;i++)
        cin>>a[i];
    sort(a,a+n);
    for(i=1;i<n;i++)
        b[i-1]=a[i]-a[i-1];
    sort(b,b+n-1);
    cout<<b[0]<<" ";
    for(i=0;i<n-2;i++,s++)
    {
        if(b[i]!=b[i+1])
            break;
    }
    cout<<s<<endl;
}

感受：

感觉挺简单。。没有难度。。