class Solution {
public:
    int triangleNumber(vector<int>& nums) {
        sort(nums.begin(), nums.end());

        vector<int> cnts(nums.back() + nums.back() + 1, 0);

        int k = 0;
        for (int i = 0; i < cnts.size(); i++) {
            while (k < nums.size() && nums[k] < i)
                k++;
            
            cnts[i] = k;
        }


        int ans = 0;

        for (int i = 0; i < nums.size() - 1; i++) {
            for (int j = i + 1; j < nums.size(); j++) {
                int part = cnts[nums[i] + nums[j]] - j - 1;
                ans += part > 0 ? part : 0;

            }
        }

        return ans;
    }
};