Two Permutations
Description
You are given three integers $n$, $a$, and $b$. Determine if there exist two permutations $p$ and $q$ of length $n$, for which the following conditions hold:
- The length of the longest common prefix of $p$ and $q$ is $a$.
- The length of the longest common suffix of $p$ and $q$ is $b$.
A permutation of length $n$ is an array containing each integer from $1$ to $n$ exactly once. For example, $[2,3,1,5,4]$ is a permutation, but $[1,2,2]$ is not a permutation ($2$ appears twice in the array), and $[1,3,4]$ is also not a permutation ($n=3$ but there is $4$ in the array).
Each test contains multiple test cases. The first line contains a single integer $t$ ($1\leq t\leq 10^4$) — the number of test cases. The description of test cases follows.
The only line of each test case contains three integers $n$, $a$, and $b$ ($1\leq a,b\leq n\leq 100$).
For each test case, if such a pair of permutations exists, output "Yes"; otherwise, output "No". You can output each letter in any case (upper or lower).
Input
Each test contains multiple test cases. The first line contains a single integer $t$ ($1\leq t\leq 10^4$) — the number of test cases. The description of test cases follows.
The only line of each test case contains three integers $n$, $a$, and $b$ ($1\leq a,b\leq n\leq 100$).
Output
For each test case, if such a pair of permutations exists, output "Yes"; otherwise, output "No". You can output each letter in any case (upper or lower).
4
1 1 1
2 1 2
3 1 1
4 1 1
Yes
No
No
Yes
Note
In the first test case, $[1]$ and $[1]$ form a valid pair.
In the second test case and the third case, we can show that such a pair of permutations doesn't exist.
In the fourth test case, $[1,2,3,4]$ and $[1,3,2,4]$ form a valid pair.