### singleDivisorTriplet 
from collections import Counter
from typing import *
def f_gold(nums: List[int]) -> int:
    def check(a, b, c):
        s = a + b + c
        return sum(s % x == 0 for x in [a, b, c]) == 1
    counter = Counter(nums)
    ans = 0
    for a, cnt1 in counter.items():
        for b, cnt2 in counter.items():
            for c, cnt3 in counter.items():
                if check(a, b, c):
                    if a == b:
                        ans += cnt1 * (cnt1 - 1) * cnt3
                    elif a == c:
                        ans += cnt1 * (cnt1 - 1) * cnt2
                    elif b == c:
                        ans += cnt1 * cnt2 * (cnt2 - 1)
                    else:
                        ans += cnt1 * cnt2 * cnt3
    return ans