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문제

In ICPCCamp, people usually use coins of values $1, 2, 3, \dots, n$. 

Bobo was very poor, he had only $a_1, a_2, a_3, \dots, a_n$ coins of values $1, 2, 3, \dots, n$, respectively. He bought an item of an unknown value without making change.

The unknown item was of non-negative integer value. Find the number of possible values it may have had.

입력

The input contains zero or more test cases, and is terminated by end-of-file. For each test case:

The first line contains one integer $n$ ($1 \leq n \leq 15$).

The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($0 \leq a_i \leq 10^9$). 

It is guaranteed that the number of test cases does not exceed $100$, and there is at most one test case where $n > 10$.

출력

For each test case, output an integer which denotes the number of possibilities.

예제 입력 1

3
0 1 2
3
0 2 3

예제 출력 1

6
12