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.