Score: $400$ points

问题陈述

有一个 $N$ 行 $N$ 列的棋盘。用 $(i, j)$ 表示从顶部数第 $i$ 行，从左边数第 $j$ 列的方格。 现在你将在棋盘上放置棋子。有两种类型的棋子，分别称为 车 和 兵。 当棋子的放置满足以下条件时，称为一个 好的排列：

• 每个方格上放置的棋子数量为零或一。
• 如果在 $(i, j)$ 处有一个车，那么对于所有 $k$ $(1 \leq k \leq N)$ 其中 $k \neq j$，$(i, k)$ 处没有棋子。
• 如果在 $(i, j)$ 处有一个车，那么对于所有 $k$ $(1 \leq k \leq N)$ 其中 $k \neq i$，$(k, j)$ 处没有棋子。
• 如果在 $(i, j)$ 处有一个兵，并且 $i \geq 2$，那么 $(i-1, j)$ 处没有棋子。

在棋盘上以好的排列放置所有的 $A$ 个车和 $B$ 个兵是否可能？

给出了 $T$ 个测试用例；解决每一个。

以上为大语言模型 kimi 翻译，仅供参考。

Problem Statement

There is a chessboard with $N$ rows and $N$ columns. Let $(i, j)$ denote the square at the $i$-th row from the top and the $j$-th column from the left.
You will now place pieces on the board. There are two types of pieces, called rooks and pawns.
A placement of pieces is called a good arrangement when it satisfies the following conditions:

• Each square has zero or one piece placed on it.
• If there is a rook at $(i, j)$, there is no piece at $(i, k)$ for all $k$ $(1 \leq k \leq N)$ where $k \neq j$.
• If there is a rook at $(i, j)$, there is no piece at $(k, j)$ for all $k$ $(1 \leq k \leq N)$ where $k \neq i$.
• If there is a pawn at $(i, j)$ and $i \geq 2$, there is no piece at $(i-1, j)$.

Is it possible to place all $A$ rooks and $B$ pawns on the board in a good arrangement?

You are given $T$ test cases; solve each of them.

Constraints

• $1 \leq T \leq 10^5$
• $1 \leq N \leq 10^4$
• $0 \leq A, B$
• $1 \leq A + B \leq N^2$
• All input values are integers.

Input

The input is given from Standard Input in the following format. Here, $\mathrm{case}_i$ represents the $i$-th case.

$T$

$\mathrm{case}_1$

$\mathrm{case}_2$

$\vdots$

$\mathrm{case}_T$

Each test case is given in the following format.

$N$ $A$ $B$

Output

Print $T$ lines. The $i$-th line should contain the answer for the $i$-th test case.
For each test case, print Yes if it is possible to place the pieces in a good arrangement and No otherwise.

Sample Input 1

8
5 2 3
6 5 8
3 2 2
11 67 40
26 22 16
95 91 31
80 46 56
998 2 44353

Sample Output 1

Yes
No
No
No
Yes
No
Yes
Yes

In the first test case, for example, you can place rooks at $(1, 1)$ and $(2, 4)$, and pawns at $(3, 3)$, $(4, 2)$, and $(5, 3)$ to have all the pieces in a good arrangement.
In the second test case, it is impossible to place all the pieces in a good arrangement.