Nuts#8769

Nuts

1 second
128 megabytes
Hard

Today, Sema and Yura attended the closing ceremony of one Olympiad. On the holiday tables there were plates of nuts. The -th plate contains a_i nuts.

In one minute Sema can choose some plates and a certain number , after which from each selected plate he picks up exactly nuts (of course, each selected plate should have at least nuts).

Determine in what minimum number of minutes all the nuts will be in Sema's pocket.

Input

The first line contains one integer (1 \le n \le 50) - the number of plates with nuts.

Second line contains integers a_1, a_2, \ldots, a_n (1 \le a_i \le 50) - the number of the nuts in the -th plate.

Output

Print a single number - the required minimum number of minutes.

Examples

Example 1

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