Problem 1028. -- Ignatius and the Princess III

## HDU_1028: Ignatius and the Princess III

Time Limit: 1000 MS  Memory Limit: 32 MB   64bit IO Format: %I64d
Submitted: 12  Accepted: 11
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## Description

"Well, it seems the first problem is too easy. I will let you know how foolish you are later." feng5166 says.

"The second problem is, given an positive integer N, we define an equation like this:
N=a+a+a+...+a[m];
a[i]>0,1<=m<=N;
My question is how many different equations you can find for a given N.
For example, assume N is 4, we can find:
4 = 4;
4 = 3 + 1;
4 = 2 + 2;
4 = 2 + 1 + 1;
4 = 1 + 1 + 1 + 1;
so the result is 5 when N is 4. Note that "4 = 3 + 1" and "4 = 1 + 3" is the same in this problem. Now, you do it!"

## Input

The input contains several test cases. Each test case contains a positive integer N(1<=N<=120) which is mentioned above. The input is terminated by the end of file.

## Output

For each test case, you have to output a line contains an integer P which indicate the different equations you have found.

## Sample Input 4
10
20

## Sample Output

5
42
627

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