Merge Triplets to Form Target Triplet

lcpy gen -n 1899   # by problem number
lcpy gen -s merge_triplets_to_form_target_triplet   # by problem name

Input: triplets = [[2,5,3],[1,8,4],[1,7,5]], target = [2,7,5]
Output: true
Explanation: Perform the following operations:
- Choose the first and last triplets [[2,5,3],[1,8,4],[1,7,5]]. Update the last triplet to be [max(2,1), max(5,7), max(3,5)] = [2,7,5]. triplets = [[2,5,3],[1,8,4],[2,7,5]].
The target triplet [2,7,5] is now an element of triplets.

Input: triplets = [[3,4,5],[4,5,6]], target = [3,2,5]
Output: false
Explanation: It is impossible to have [3,2,5] as an element because there is no 2 in any of the triplets.

Input: triplets = [[2,5,3],[2,3,4],[1,2,5],[5,2,3]], target = [5,5,5]
Output: true
Explanation: Perform the following operations:
- Choose the first and third triplets [[2,5,3],[2,3,4],[1,2,5],[5,2,3]]. Update the third triplet to be [max(2,1), max(5,2), max(3,5)] = [2,5,5]. triplets = [[2,5,3],[2,3,4],[2,5,5],[5,2,3]].
- Choose the third and fourth triplets [[2,5,3],[2,3,4],[2,5,5],[5,2,3]]. Update the fourth triplet to be [max(2,5), max(5,2), max(5,3)] = [5,5,5]. triplets = [[2,5,3],[2,3,4],[2,5,5],[5,5,5]].
The target triplet [5,5,5] is now an element of triplets.

class Solution:
    # Time: O(n)
    # Space: O(1)
    def merge_triplets(self, triplets: list[list[int]], target: list[int]) -> bool:
        tx, ty, tz = target
        found_x = found_y = found_z = False

        for a, b, c in triplets:
            # Skip any triplet that would push a component past the target.
            if a > tx or b > ty or c > tz:
                continue
            if a == tx:
                found_x = True
            if b == ty:
                found_y = True
            if c == tz:
                found_z = True
            if found_x and found_y and found_z:
                return True

        return found_x and found_y and found_z