Minimum Days to Deliver Parcels

Each day, choose a positive integer x and ship exactly x parcels from every center that still has parcels. x cannot exceed the current remaining amount of any non-empty center, and empty centers do not take part. Find the minimum number of days to ship all parcels. If everything is 0 at the start, the answer is 0 days.

输入格式

The first line contains n and the second line contains parcels. 1≤n≤1000000, 0≤parcels[i]≤10^9; the original million-sized range is kept.

输出格式

Output a single integer, the answer.

样例 1

输入：

5
2 3 4 3 3

输出：

3

样例 2

输入：

3
3 3 3

输出：

1

样例 3

输入：

2
0 0

输出：

0

样例说明

The answers are 3, 1 and 0 respectively. In the first example you can ship 2, 1 and then 1 parcels from every non-empty center.