Roger has a list of positive integers . However, his list is not yet finalized. Some of these numbers are wildcards which will be represented as zeroes in the list. Roger will try to assign the wildcards a value so that
- The list is sorted from least to greatest
- All wildcards have the same value, which is a positive integer
Help Roger find out if this is possible. Output
YES if he can assign the wildcards a value so that is sorted and
If , then it is a wildcard, otherwise .
The first line contains a single integer .
The next line contains space-separated integers, .
Output a single string:
YES if it is possible and
Subtask 1 [30%]
Subtask 2 [30%]
Subtask 3 [40%]
Sample Input 1
6 0 0 1 5 5 5
Sample Output 1
Explanation for Sample Input 1
The first two elements are wildcards. Setting them to gives a sorted list.
Sample Input 2
6 1 5 5 5 5 1
Sample Output 2
Explanation for Sample 2
There are no wildcards, so Roger cannot do anything. is not sorted so the answer is no.
Sample Input 3
6 1 0 2 0 3 0
Sample Output 3