Soldier and Badges

Description

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.

Sample Input

Input

41 3 1 4

Output

1

Input

51 2 3 2 5

Output

2

Hint

In first sample test we can increase factor of first badge by 1.

In second sample test we can increase factors of the second and the third badge by 1.

题目解析：第一个数n代表下面有多少个数，接着输入n个数，变化数字的大小知道所有的数都不相等。

题目链接：http://codeforces.com/problemset/problem/546/B

源代码：

#include<cstdio>#include<iostream>#include<algorithm>#include<cstring>using namespace std;int main(){    int n,a[4000],ans=0,i;    scanf("%d",&n);    for(i=0;i<n;i++)        scanf("%d",&a[i]);    sort(a,a+n);    for(i=0;i<n-1;i++)    {        while(a[i+1]<=a[i])        {            a[i+1]=a[i+1]+1;            ans++;        }    }    printf("%d\n",ans);    return 0;}