# codeforce 1041a heist (水) no.15

## Heist

There was an electronic store heist last night.

All keyboards which were in the store yesterday were numbered in ascending order from some integer number x. For example, if x=4 and there were 3 keyboards in the store, then the devices had indices 4, 5, 6, and if x=10 and there were 7 of them then the keyboards had indices 10,11, 12, 13, 14, 15 and 16.

After the heist, only n keyboards remain, and they have indices a1,a2…,an. Calculate the minimum possible number of keyboards that have been stolen. The staff remember neither x nor the number of keyboards in the store before the heist.

#### Input

The first line contains single integer n (1≤n≤1000) — the number of keyboards in the store that remained after the heist.

The second line contains n distinct integers a1,a2,…,an (1≤ai≤10^9) — the indices of the remaining keyboards. The integers ai are given in arbitrary order and are pairwise distinct.

#### Output

Print the minimum possible number of keyboards that have been stolen if the staff remember neither x nor the number of keyboards in the store before the heist.

input

4
10 13 12 8

output

2

input

5
7 5 6 4 8

output

0

#### Note

In the first example, if x=8 then minimum number of stolen keyboards is equal to 2. The keyboards with indices 9 and 11 were stolen during the heist.
In the second example, if x=4 then nothing was stolen during the heist.