CF1811D.Umka and a Long Flight

The girl Umka loves to travel and participate in math olympiads. One day she was flying by plane to the next olympiad and out of boredom explored a huge checkered sheet of paper.

Denote the $n$-th Fibonacci number as $F_n = \begin{cases} 1, & n = 0; \\ 1, & n = 1; \\ F_{n-2} + F_{n-1}, & n \ge 2. \end{cases}$

A checkered rectangle with a height of $F_n$ and a width of $F_{n+1}$ is called a Fibonacci rectangle of order $n$.

Umka has a Fibonacci rectangle of order $n$. Someone colored a cell in it at the intersection of the row $x$ and the column $y$.

It is necessary to cut this rectangle exactly into $n+1$ squares in such way that

• the painted cell was in a square with a side of $1$;
• there was at most one pair of squares with equal sides;
• the side of each square was equal to a Fibonacci number.

Will Umka be able to cut this rectangle in that way?

女孩乌姆卡热爱旅行和参加数学奥林匹克竞赛。一天，她乘飞机前往下一场奥赛，在无聊之际，开始研究一张巨大的方格纸。

记第 $n$ 个斐波那契数为

$$F_n = \begin{cases} 1, & n = 0; \\ 1, & n = 1; \\ F_{n-2} + F_{n-1}, & n \ge 2. \end{cases}$$

一个高为 $F_n$、宽为 $F_{n+1}$ 的方格矩形被称为 $n$ 阶斐波那契矩形。

乌姆卡有一个 $n$ 阶斐波那契矩形。某人将其中位于第 $x$ 行、第 $y$ 列的方格涂上了颜色。

现在需要将该矩形恰好切成 $n+1$ 个正方形，使得：

• 被涂色的方格位于一个边长为 $1$ 的正方形内；
• 所有正方形中，至多有一对正方形边长相等（即其余所有正方形边长互不相同）；
• 每个正方形的边长均为某个斐波那契数。

乌姆卡能否以这种方式完成切割？

The first line contains an integer $t$ ($1 \le t \le 2 \cdot 10^5$) — number of test cases.

For each test case the integers $n$, $x$, $y$ are given ($1 \le n \le 44$, $1 \le x \le F_n$, $1 \le y \le F_{n+1}$) — the order of the Fibonacci rectangle and the coordinates of the colored cell.

第一行包含一个整数 $t$（$1 \le t \le 2 \cdot 10^5$）—— 测试用例的数量。

对于每个测试用例，给定整数 $n$、$x$、$y$（$1 \le n \le 44$，$1 \le x \le F_n$，$1 \le y \le F_{n+1}$）—— 斐波那契矩形的阶数以及着色单元格的坐标。

For each test case, print "YES" if the answer is positive, and "NO" otherwise.

You can print "YES" and "NO" in any case (for example, the strings "yEs", "yes" and "Yes" will be recognized as a positive answer).

对于每个测试用例，如果答案为肯定，则输出 “YES”；否则输出 “NO”。

“YES” 和 “NO” 可以以任意大小写形式输出（例如，字符串 “yEs”、“yes” 和 “Yes” 均被视为肯定回答）。

The first, third and fourth test cases.

第一、第三和第四个测试用例。