Maximize Final Element

You may rearrange the array arbitrarily and decrease elements to integers of at least 1. The final first element must be 1, and a[i]−a[i−1]≤1 must hold for i≥1; find the maximum value of the last element. This is a one-sided difference condition, and the original array need not be sorted.

输入格式

The first line contains n; the second line contains the array. The original text had no numeric bounds; this site uses 1≤n≤200000, 1≤element≤10^9.

输出格式

Output a single integer, the answer.

样例 1

输入：

4
3 1 3 4

输出：

4

样例 2

输入：

1
100

输出：

1

样例 3

输入：

3
1 1 10

输出：

2

样例说明

The answers are 4, 1 and 2. A single element must become 1; you cannot simply take the maximum as the answer.