Best string Orz~

Time Limit: 3000 ms Memory Limit: 65536 KiB

Problem Description

If a string S is made up by n1 'O',n2 'r', n3 'z' and n4 '~',(n1>=n2>=n3>=n4),and for all of its prefix substring C,if in C the number of 'O' is larger or equal than the number of 'r',the number of 'r' is larger or equal than the number of 'z' and the number of 'z' is larger or equal than the number of '~',then we call it best string.(For example,the prefix substring of "Orz~" is "O","Or","Orz" and "Orz~").
Now give you the n1,n2,n3,n4,I wonder how many best strings are there with only n1 'O',n2 'r',n3 'z',n4 '~';

Input

There are more than one input.
Each input is four number n1,n2,n3,n4,end by four zeros,which shouldn\'t be processed.(0<=n1,n2,n3,n4<10)

Output

For each input,print the number of best string.

Sample Input

1 1 1 1
0 0 0 0

Sample Output

1

Hint

 

Source

SDUST