We call an quadruple of positive integers, , beautiful if the following condition is true:
Note: is the bitwise XOR operator.
Given , , , and , count the number of beautiful quadruples of the form where the following constraints hold:
When you count the number of beautiful quadruples, you should consider two quadruples as same if the following are true:
- They contain same integers.
- Number of times each integers occur in the quadruple is same.
For example and should be considered as same.
Input Format
A single line with four space-separated integers describing the respective values of , , , and .
Constraints
- For of the maximum score,
Output Format
Print the number of beautiful quadruples.
Sample Input
1 2 3 4
Sample Output
11
Explanation
There are beautiful quadruples for this input:
Thus, we print as our output.
Note that is same as .