923. 3Sum With Multiplicity

class Solution:
    def threeSumMulti(self, arr: List[int], target: int) -> int:
        MOD = 10**9 + 7
        # 0 <= arr[i] <= 100
        count = [0] * 101
        # num of occurrency every number in arr
        for x in arr:
            count[x] += 1
        res = 0
        # all same
        if target % 3 == 0:
            x = target // 3
            if 0<=x<=100:
                res += count[x] * (count[x]-1) * (count[x]-2) / 6
                res %= MOD
        # all different
        for x in range(101):
            for y in range(x+1, 101):
                z = target - x - y
                if y < z <= 100:
                    res += count[x] * count[y] * count[z]
                    res %= MOD
        # x == y != z
        for x in range(101):
            z = target - 2 * x
            if x < z <= 100:
                res += (count[x] * (count[x] - 1) / 2) * count[z]
                res %= MOD
        # x != y == z
        for x in range(101):
            if (target - x) % 2 == 0:
                y = (target - x) // 2
                if x < y <= 100:
                    res += (count[y] * (count[y] - 1) / 2) * count[x]
                    res %= MOD
        return int(res)