Educational Codeforces Round 34 D. Almost Difference【模拟/stl-map/ long double】

D. Almost Difference

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

Let's denote a function

You are given an array a consisting of n integers. You have to calculate the sum of d(ai, aj) over all pairs (i, j) such that 1 ≤ i ≤ j ≤ n.

Input

The first line contains one integer n (1 ≤ n ≤ 200000) — the number of elements in a.

The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 109) — elements of the array.

Output

Print one integer — the sum of d(ai, aj) over all pairs (i, j) such that 1 ≤ i ≤ j ≤ n.

Examples

input

5
1 2 3 1 3

output

4

input

4
6 6 5 5

output

0

input

4
6 6 4 4

output

-8

Note

In the first example:

1. d(a1, a2) = 0;
2. d(a1, a3) = 2;
3. d(a1, a4) = 0;
4. d(a1, a5) = 2;
5. d(a2, a3) = 0;
6. d(a2, a4) = 0;
7. d(a2, a5) = 0;
8. d(a3, a4) =  - 2;
9. d(a3, a5) = 0;
10. d(a4, a5) = 2.

【题意】：计算每个数贡献的值之和。贡献规则如上分段函数所示。

【分析】：假设第i位值是a，那么他的贡献tmp=a*(i-1)-presum。tmp是假设都计算为y-x，presum是前缀和。那最后的贡献就是tmp-cnt(a-1)+cnt(a+1)，相邻的数去掉。因为相邻的数和本身总是相差1，符合分段函数归0部分。前面出现过多少次a-1，a+1，用map实现。

【代码】：

#include <bits/stdc++.h>
using namespace std;
map<double,double>a;
int main()
{
    int n;
    scanf("%d",&n);
    long double ans=;
    for (int i=;i<n;i++)
    {
        double x;scanf("%lf",&x);
        a[x]++;
        ans= ans+ a[x+]-a[x-]+x*(i+-n+i);
    }
    cout << fixed << setprecision() << ans << endl;
    return ;
}