Box Stack II

import sys
import bisect

def max_pyramid_height(n, boxes):
    boxes.sort(key=lambda x: (x[0], x[1]))
    
    sorted_second_dims = sorted(list(set(box[1] for box in boxes)))
    compressed = {y: i+1 for i, y in enumerate(sorted_second_dims)}  

    size = len(sorted_second_dims) + 2
    BIT = [0] * size
    
    def update(index, value):
        while index < size:
            if BIT[index] < value:
                BIT[index] = value
            else:
                break  
            index += index & -index
    
    def query(index):
        result = 0
        while index > 0:
            if BIT[index] > result:
                result = BIT[index]
            index -= index & -index
        return result
    
    max_height = 0
    for box in boxes:
        _, y, h = box
        idx = compressed[y]
        best = query(idx)
        current_height = best + h
        if current_height > max_height:
            max_height = current_height
        update(idx, current_height)
    
    return max_height

def main():
    import sys
    input = sys.stdin.read
    data = input().split()
    n = int(data[0])
    boxes = []
    index = 1
    for _ in range(n):
        first_dim = int(data[index])
        second_dim = int(data[index + 1])
        height = int(data[index + 2])
        boxes.append((first_dim, second_dim, height))
        index += 3
    print(max_pyramid_height(n, boxes))

if __name__ == "__main__":
    main()

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