God knows why somewhat more efficient way of extending Subset Sum Problem to broadcasted sum of 2d vectors in Python

ssp_2d.py

from functools import reduce
from itertools import combinations

from operator import add

array = [(1, 0, 0), (0, 1, 0), (0, 0, 1), (1, 0, 1)]
target = (1, 1, 1)

def broadcast_sum(*args: tuple[int, ...]) -> tuple[int, ...]:
    return reduce(lambda a, b: tuple(map(add, a, b)), args, (0,) * len(args[0]))

result = [tuple(idx) for i in range(1, len(array) + 1) for seq, idx in zip(combinations(array, i), combinations(range(0, len(array), 1), i)) if broadcast_sum(*seq) == target]
print(result) # [(1, 3), (0, 1, 2)]
print(len(result)) # 2