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B. Soldier and Badges

time limit per test

3 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputColonel 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.

Examples

Input

4

1 3 1 4

Output

1

Input

5

1 2 3 2 5

Output

2

Note

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.

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

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