Problem 1023 --#551. 「LibreOJ Round #8」Matrix

## 1023: #551. 「LibreOJ Round #8」Matrix

Time Limit: 1 Sec  Memory Limit: 256 MB
Submit: 0  Solved: 0
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## Description

Alex 在和 Ball 玩游戏，他们面前有一个 n×nn \times n 的空白矩阵 MM，Alex 和 Ball 轮流往上放标记，Ball 先手

⌊n2/2⌋\lfloor n^2 /2 \rfloor 轮后，若 Alex 没有获胜，则 Ball 获胜。

• Alex 在自己每次操作前记得双方之前所有操作的情况下是否有必胜策略。
• Alex 在自己每次操作前忘掉双方之前所有操作，仅知道 Ball 最后一次操作的情况下是否有必胜策略。

Ball 永远记得双方的所有操作。

Alex is playing a game with Ball. There is a blank matrix MM with nn lines and nn columns. Alex and Ball take turns to mark one of the matrix elements with his own sign (Alex’s sign is called AA and Ball’s sign is called BB). Ball goes first.
After a round of game (a round means that Ball and Alex operates once each in order), if there exists a permutation p[1..n]p[1..n] satisfies that for each i∈[1,n] i \in [1,n],M[i][p[i]]=AM[i][p[i]]=A, Alex wins immediately.
After ⌊n2/2⌋\lfloor n^2 /2 \rfloor rounds, if Alex hasn’t won, Ball wins instead.
Notice that whenever anyone tries to mark a marked matrix element(because of forgetting), he will lose the game immediately.
Sly Ball thinks of a way to interfere Alex. He decides to operate long time after the Alex’s last operation so that Alex may forget about the previous operations.
Now you get this message and want to know two things for a given nn:

• whether Alex has winning strategy if he remembers all the previous operations
• whether Alex has winning strategy if he forgets all the previous operations, and only knows Ball's last operation each time.

Ball always knows all their previous operations.

#### 输入格式

This first line contains a single integer TT which means the number of the test cases.
The following TT lines, each line contains one integer nn which means the size of the matrix.

#### 输出格式

Write to the standard output.
For each test case, output two lines of Yes or No.
The first line means whether Alex can win for sure If he remembers the previous operations.
The second line means whether Alex can win for sure If he forgets the previous operations.

#### 样例输入

2
1
2

#### 样例输出

No
No
No
No

#### Sample Input

2
1
2

#### Sample Output

No
No
No
No

#### 数据范围与提示

11 10 ≤3\leq 3
22 40 ≤100\leq 100
33 20 ≤106\leq 10^6
44 30 ≤1018\leq 10^{18}

For all test cases, 1≤n≤10181\leq n \leq 10^{18},1≤T≤1001 \leq T \leq 100 .

Detailed constraints and hints are as follows (blank grids denote the same constraints as mentioned above):