Score : $400$ points

问题描述

给定一个包含 $N$ 个正整数的序列：$A = (A_1, A_2, \dots, A_N)$。确定是否存在满足所有条件的一对序列 $B = (B_1, B_2, \dots, B_x), C = (C_1, C_2, \dots, C_y)$，如果存在，则打印出这样一对序列。

• $1 ≤ x, y ≤ N$。
• $1 \le B_1 < B_2 < \dots < B_{x} \le N$。
• $1 \le C_1 < C_2 < \dots < C_{y} \le N$。
• 序列 $B$ 和 $C$ 不相同。
  • 在这里，当 $x ≠ y$ 或存在一个整数 $i\ (1 ≤ i ≤ \min(x, y))$ 使得 $B_i ≠ C_i$ 时，我们认为 $B$ 和 $C$ 是不同的序列。
• $A_{B_1} + A_{B_2} + \dots + A_{B_x}$ 与 $A_{C_1} + A_{C_2} + \dots + A_{C_y}$ 对 $200$ 取模后的结果相等。

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

You are given a sequence of $N$ positive integers: $A = (A_1, A_2, \dots, A_N)$. Determine whether there is a pair of sequences $B = (B_1, B_2, \dots, B_x), C = (C_1, C_2, \dots, C_y)$ satisfying all of the conditions, and print one such pair if it exists.

• $1 ≤ x, y ≤ N$.
• $1 \le B_1 < B_2 < \dots < B_{x} \le N$.
• $1 \le C_1 < C_2 < \dots < C_{y} \le N$.
• $B$ and $C$ are different sequences.
  • Here, we consider $B$ and $C$ different when $x ≠ y$ or there is an integer $i\ (1 ≤ i ≤ \min(x, y))$ such that $B_i ≠ C_i$.
• $A_{B_1} + A_{B_2} + \dots + A_{B_x}$ and $A_{C_1} + A_{C_2} + \dots + A_{C_y}$ are equal modulo $200$.

Constraints

• All values in input are integers.
• $2 \le N \le 200$
• $1 \le A_i \le 10^9$

Input

Input is given from Standard Input in the following format:

$N$

$A_1$ $A_2$ $\dots$ $A_N$

Output

If there is no pair of sequences $B, C$ satisfying the conditions, print a single line containing No.

Otherwise, print your choice of $B$ and $C$ in the following format:

Yes

$x$ $B_1$ $B_2$ $\dots$ $B_x$

$y$ $C_1$ $C_2$ $\dots$ $C_y$

The checker is case-insensitive: you can use either uppercase or lowercase letters.

Sample Input 1

5
180 186 189 191 218

Sample Output 1

Yes
1 1
2 3 4

For $B=(1),C=(3,4)$, we have $A_1 = 180,\ A_3 + A_4 = 380$, which are equal modulo $200$. There are other solutions that will also be accepted, such as:

yEs
4 2 3 4 5
3 1 2 5

Sample Input 2

2
123 523

Sample Output 2

Yes
1 1
1 2

Sample Input 3

6
2013 1012 2765 2021 508 6971

Sample Output 3

No

If there is no pair of sequences satisfying the conditions, print a single line containing No.

update @ 2024/3/10 09:11:52