Max Batches For Shipment

Each category has inventory[i] items. Each batch uses at most one item per category, and each batch must contain strictly more items than the previous one; each item can be used at most once, and leftovers are allowed. Find the maximum number of batches.

输入格式

The first line contains n; the second line contains the inventories. The original text had no numeric bounds; this site uses 1≤n≤200000, 0≤inventory[i]≤10^9.

输出格式

Output a single integer, the answer.

样例 1

输入：

5
2 3 1 4 2

输出：

4

样例 2

输入：

3
100 1 1

输出：

2

样例 3

输入：

3
0 0 0

输出：

0

样例说明

The answers are 4, 2 and 0. Even with a large total, the two of the three categories that have only one item each cannot both supply the second and the third batches.