Given an array A of n integers. Count the number of sets (i,j,k) that i<j<k and edges of length Ai,Aj,Ak can form an triangle.
For example, you can't form an triangle out of three edges of length 1,2,4.
### Input
- The first line contains an integer n.
- The second line contains n integer Ai.
### Output
- The number of sets (i,j,k) which can form an triangle.
### Constraints
- 1≤n≤1500.
- 1≤Ai≤109.
### Example
Input:
41234
Output:
1