A. Two Permutationstime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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).InputEach 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).OutputFor 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).ExampleInput
41 1 12 1 23 1 14 1 1Output
Yes
No
No
Yes
NoteIn 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.
41 1 12 1 23 1 14 1 1
Yes No No Yes 
['brute force', 'constructive algorithms', '*800']