Overview

Since the number of doors you can choose in each room is independent, the number of paths from the entrance to the exit is “the product of the number of doors in each room.”
In other words, the answer is \(A_1 \times A_2 \times \cdots \times A_N\).

Analysis

The essence of this problem is that the choices in each room are independent of each other.

• Room 1 has \(A_1\) choices
• Room 2 has \(A_2\) choices
• …
• Room \(N\) has \(A_N\) choices

Therefore, by the rule of product, the total number of paths is $\( A_1 \times A_2 \times \cdots \times A_N \)$

For example, if \(N=3, (A_1,A_2,A_3)=(2,3,4)\), then: - Room 1: 2 choices - Room 2: 3 choices - Room 3: 4 choices
So the total is \(2 \times 3 \times 4 = 24\) paths.

Why naive enumeration doesn’t work

If you actually enumerate all paths, the number can be as large as \(10^{18}\) in the worst case, which is not feasible.
However, since we only need “the number of paths,” it is sufficient to compute the product without enumeration.

Algorithm

1. Initialize ans = 1.
2. For each \(i=1..N\), multiply the input value \(A_i\) into ans.
3. Output ans at the end.

That alone gives the correct answer.

Complexity

• Time complexity: \(O(N)\)
• Space complexity: \(O(1)\) (since we process the input sequentially)

Implementation Notes

• According to the constraints, the final product is at most \(10^{18}\), so there is no concern about overflow (in Python, arbitrary-precision integers are supported natively).

• Since the input can have up to \(10^5\) lines, using sys.stdin.readline is a fast and safe implementation choice.

  Source Code

import sys

def main():
    input = sys.stdin.readline
    N = int(input().strip())
    ans = 1
    for _ in range(N):
        ans *= int(input().strip())
    print(ans)

if __name__ == "__main__":
    main()

This editorial was generated by gpt-5.3-codex.