又一道動態規劃算法題

Ignatius and the Princess III

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)

Problem 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[1]+a[2]+a[3]+...+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 indicates the different equations you have found.

 

Sample Input

4

10

20

 

Sample Output

5

42

627

 

問題是這樣的，給定一個正整數N（小於等於120），如N=3，則N可以表示爲1+1+1，1+2和3，這三種正整數相加的形式。注意，1+2和2+1被視爲是一種。要求輸出N共有幾組這樣的表達式。又比如，4可以表示爲1+1+1+1，1+1+2，1+3，2+2和4，這五種表達式，所以輸入是4，輸出是5。