Salesforce's Case Management System now operates at a massive scale, processing up to a million cases per batch. To assign work efficiently, the operations team must quickly find distinct pairs of cases whose combined resolution times (in minutes) are a non-zero multiple of 60. Pairs are considered distinct by their indices. If two cases share the same resolution time, choosing a different index yields a new pair.

Example n = 3 resolutionTimes = [30, 30, 60]

Only one valid pair, indices (0, 1), sums to 60. Return 1.

Function Description Complete the function multipleSums in the editor below.

• multipleSums(int resolutionTimes[n]) — list of integers representing case-resolution times

Returns

• long: the number of valid pairs whose sum is a non-zero multiple of 60

Constraints

• 1 <= n <= 10^6
• 1 <= resolutionTimes[i] <= 10^9
• The answer can be as large as n * (n - 1) / 2; store and return it in 64-bit (long) precision.
• Your algorithm must run in O(n) time and use at most O(60) additional space.

Note:

• The sum must be a non-zero multiple of 60; ignore pairs that sum to 0.
• An efficient strategy counts how many times each remainder r = t mod 60 occurs, then uses combinatorics to total all valid pairings.

Sample Case 0

Sample Input For Custom Testing 4 4 20 60 120

(Which translates to n = 4 and resolutionTimes = [20, 40, 60, 120])

Sample Output 2

Explanation Valid index pairs: (0, 1) and (2, 3).