codeforces#P1761A. Two Permutations

Two Permutations

Description

You are given three integers nn, aa, and bb. Determine if there exist two permutations pp and qq of length nn, for which the following conditions hold:

  • The length of the longest common prefix of pp and qq is aa.
  • The length of the longest common suffix of pp and qq is bb.

A permutation of length nn is an array containing each integer from 11 to nn exactly once. For example, [2,3,1,5,4][2,3,1,5,4] is a permutation, but [1,2,2][1,2,2] is not a permutation (22 appears twice in the array), and [1,3,4][1,3,4] is also not a permutation (n=3n=3 but there is 44 in the array).

Each test contains multiple test cases. The first line contains a single integer tt (1t1041\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 nn, aa, and bb (1a,bn1001\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 tt (1t1041\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 nn, aa, and bb (1a,bn1001\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).

输入数据 1

4
1 1 1
2 1 2
3 1 1
4 1 1

输出数据 1

Yes
No
No
Yes

Note

In the first test case, [1][1] and [1][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][1,2,3,4] and [1,3,2,4][1,3,2,4] form a valid pair.