Definitions

• Permutation: level contains n distinct integers (commonly the numbers 1..n exactly once).
• Team (size 4): choose indices (x, y, z, w) such that x < y < z < w (indices are 0-based).
• Productive team condition: level[x] < level[z] and level[y] > level[w].

Task

Return the total number of productive teams (x, y, z, w) that satisfy:

• x < y < z < w
• level[x] < level[z]
• level[y] > level[w]

Input / Output

• Input: integer array level (a permutation), length n.
• Output: an integer = number of productive teams of size 4.

Examples

Example 1

level = [1, 4, 2, 3, 5]

Valid productive teams count = 1

Explanation (one productive team):

• Choose indices (x, y, z, w) = (0, 1, 2, 3) → values [level[0], level[1], level[2], level[3]] = [1, 4, 2, 3]
• level[x] < level[z] → 1 < 2 ✅
• level[y] > level[w] → 4 > 3 ✅

Example 2

level = [1, 5, 2, 4, 3]

Output: 3

Explanation (productive teams):

• (0, 1, 2, 3) → values [1, 5, 2, 4]
• (0, 1, 2, 4) → values [1, 5, 2, 3]
• (0, 1, 3, 4) → values [1, 5, 4, 3]

Example 3

level = [4, 3, 2, 1]

Output: 0

Explanation: the only possible quadruple is (0,1,2,3), but level[0] < level[2] is 4 < 2, which is false.

Constraints

• 4 ≤ n ≤ 3000
• level is a permutation (all elements are distinct; commonly 1..n)