Maximize Beauty

The beauty of an array is the number of 1-based positions i with arr[i]=i. You may repeatedly delete any element, as long as the array keeps a length of at least 1, and the order does not change. Find the maximum possible beauty.

This site uses a standard input/output protocol.

输入格式

The first line contains n; the second line contains n positive integers. 1≤n≤2000, 1≤arr[i]≤10^5.

输出格式

Output the maximum beauty.

样例 1

输入：

7
1 3 2 5 4 5 3

输出：

4

样例 2

输入：

6
6 3 2 4 3 4

输出：

3

样例 3

输入：

1
7

输出：

0

样例 4

输入：

3
2 2 2

输出：

1