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Arrange Balls
Medium Accuracy: 72.86% Submissions: 118 Points: 4

There are p balls of type P, q balls of type Q and r balls of type R. Using the balls we want to create a straight line such that no two balls of same type are adjacent.

Example 1:

Input: p = 2, q = 2, r = 2
Output: 30
Explanation: There are 30 possible arrangements
of balls. Some of them are PQR, PRQ, PRP, PRQ,
PQR,...


Example 2:

Input: p = 1, q = 1, r = 1
Output: 6
Explanation: There are 6 possible arrangements
and these are PQR, PRQ, QPR, QRP, RPQ, RQP.


You don't need to read or print anything. Your task is to complete the function CountWays() which takes count of P type balls, Q type balls and R type balls and returns total number of possible arrangements such that no two balls of same type are adjacent modulo 109 + 7.

Expected Time Complexity: O(N3) where N = max(p, q, r)
Expected Space Complexity: O(N3)

Constranits:
1 <= p, q, r <= 100

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