package main

// idk complexity
func multiply(num1 string, num2 string) string {
	l1, l2 := len(num1), len(num2)
	to_sum := make(map[int]int)
	max_p10 := 0
	for p1 := l1 - 1; p1 >= 0; p1-- {
		for p2 := l2 - 1; p2 >= 0; p2-- {
			n1, n2 := int(num1[p1])-48, int(num2[p2])-48
			p10 := l1 - 1 - p1 + l2 - 1 - p2
			d := n1 * n2
			if p10 > max_p10 {
				max_p10 = p10
			}
			to_sum[p10] = to_sum[p10] + d
		}
	}
	sum := ""
	for p := 0; p <= max_p10; p++ {
		d := to_sum[p]
		sum = string(48+(d%10)) + sum
		to_sum[p+1] = to_sum[p+1] + d/10
		if p+1 > max_p10 && d/10 > 0 {
			max_p10 = p + 1
		}
	}
	for len(sum) > 1 && sum[0] == '0' {
		sum = sum[1:]
	}
	return sum
}

func main() {
	println(multiply("123456", "0"))
}