As the Queen's chief technologist, you have been tasked with organising the army's newest cutting edge1 division: the cavalry.
Naturally, the Queen is sceptical, so to prove it's worth it you are going to conduct a quick field test. Firstly, you will need to group your knights into squads.
Unfortunately, the N knights in your division are very inexperienced, having only been training for two weeks! The ith knight (counting from 1) has told you that they would only be comfortable in a squad containing exactly ai knights.
You can make as many or as few squads as you like of any size, so long as every knight is comfortable.
After feeding your whining, whinnying horses their pheasant-based supper, you return to your lonely lodge to determine if it is possible to divide up your cavalry.
The first line of input will contain N, the number of knights in your division.
Then, N lines will follow. The ith line (counting from 1) will contain ai, the size of the squad the ith knight wants to join.
5 2 3 2 3 3
3 2 2 2
In the first case, you can put knights 1 and 3 in one squad, and knights
2, 4 and 5 into a second one. This makes them all comfortable, so the
answer is YES.
In the second case, you can put knights 1 and 2 together in the same squad, but then knight 3 cannot form a squad by themselves (since knight 3 wants to be in a squad of size 2). No matter what you do, one of the knights is going to get left out, so the answer is NO.
For all subtasks, 1 ≤ N ≤ 100,000, and 1 ≤ ai ≤ N.