Soldier and Badges

Colonel has n badges. He wants to give one badge to every of his n soldiers. Each badge has a coolness factor, which shows how much it's owner reached. Coolness factor can be increased by one for the cost of one coin.

For every pair of soldiers one of them should get a badge with strictly higher factor than the second one. Exact values of their factors aren't important, they just need to have distinct factors.

Colonel knows, which soldier is supposed to get which badge initially, but there is a problem. Some of badges may have the same factor of coolness. Help him and calculate how much money has to be paid for making all badges have different factors of coolness.

Input

First line of input consists of one integer n (1 ≤ n ≤ 3000).

Next line consists of n integers a_i (1 ≤ a_i ≤ n), which stand for coolness factor of each badge.

Output

Output single integer — minimum amount of coins the colonel has to pay.

Example

Input

4
1 3 1 4

Output

1

Input

5
1 2 3 2 5

Output

2

只要数据全不同就好了，我想的是用数组存完后排序，利用循环让后一个数总是大于前一个数

#include<iostream>
#include<algorithm>
using namespace std;
#define N 3005
int main()
{
    int t,a[N];
    while(cin>>t)
    {
        int count=0;
        for(int i=0;i<t;i++)
            cin>>a[i];
        sort(a,a+t);
        for(int i=1;i<t;i++)
        {
            while(a[i]<=a[i-1])
            {
                a[i]++;
                count++;
            }
        }
        cout<<count<<endl;
    }
    return 0;
}