A. Three Moves Game
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Alice and Bob are playing a game on a $$$1 \times n$$$ grid, where:

  • Alice starts at cell $$$x$$$, Bob starts at cell $$$y$$$, where $$$1 \le x,y \le n$$$ and $$$x \neq y$$$.
  • Alice and Bob alternate turns, with Alice moving first.
  • A turn consists of exactly $$$3$$$ moves, where each move is either move one unit to the left or move one unit to the right.
  • A player can't jump onto or over another player, and all moves cannot exceed the boundary.

For example, $$$n=8$$$, $$$x=4$$$ and $$$y=7$$$, where Alice moves first:

  • $$$4 \rightarrow 3 \rightarrow 2 \rightarrow 1$$$ is considered as Alice's valid moves.
  • $$$4 \rightarrow 5 \rightarrow 6 \rightarrow 5$$$ is considered as Alice's valid moves.
  • $$$4 \rightarrow 5 \rightarrow 6$$$ is considered as Alice's invalid moves because this violates the rule of exactly $$$3$$$ moves.
  • $$$4 \rightarrow 5 \rightarrow 6 \rightarrow 7$$$ is considered as Alice's invalid moves because this violates the rule that a player can't jump onto another player.

A player loses if no valid move exists on their turn. The game terminates when a player cannot move.

Your task is to determine whether Alice will win, assuming that the strategies of the two players are optimal.

Input

The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^3$$$).

The only line of each test case contains three integers $$$n$$$, $$$x$$$, and $$$y$$$ ($$$1 \le n \le 10$$$, $$$1 \le x, y \le 10$$$, $$$x \neq y$$$).

Output

For each test case, if Alice will win assuming that the strategies of the two players are optimal, output "YES" (without quotes) in a new line. Otherwise, output "NO".

Example
Input
3
2 1 2
5 1 5
10 7 3
Output
NO
YES
YES
Note

In the first test case, Alice can not do any valid move from the beginning. Thus, Alice will lose.

In the second test case, Alice can do move $$$1 \rightarrow 2 \rightarrow 3 \rightarrow 4$$$. After that, Bob can not do any valid move. Thus, Alice will win.