Get Minimum Time

Servers 1..total form a ring with unit-length edges. Choose any starting server and visit all target servers along one continuous sequential route; crossing each edge takes 1 unit of time, and this is not a simultaneous broadcast in both directions. Targets are distinct.

输入格式

The first line contains n total; the second line contains n target IDs. 1≤total≤10^9, 1≤n≤min(total,100000), 1≤ID≤total. The original constraint ID≤n conflicts with the statement and all examples, so it is restored to ≤total according to the statement.

输出格式

Output a single integer, the answer.

样例 1

输入：

3 8
2 6 8

输出：

4

样例 2

输入：

2 5
1 5

输出：

1

样例 3

输入：

1 10
4

输出：

0

样例说明

The answers are 4, 1 and 0. With a single target, simply start there.