Output
In the first line print "
YES" (without the quotes), if it is possible to come up with three distinct plans of doing the tasks. Otherwise print in the first line "
NO" (without the quotes). If three desired plans do exist, print in the second line
n distinct integers that represent the numbers of the tasks in the order they are done according to the first plan. In the third and fourth line print two remaining plans in the same form.
If there are multiple possible answers, you can print any of them.
Examples
Output
YES
1 4 2 3
4 1 2 3
4 1 3 2
Note
In the first sample the difficulty of the tasks sets one limit: tasks 1 and 4 must be done before tasks 2 and 3. That gives the total of four possible sequences of doing tasks : [1, 4, 2, 3], [4, 1, 2, 3], [1, 4, 3, 2], [4, 1, 3, 2]. You can print any three of them in the answer.
In the second sample there are only two sequences of tasks that meet the conditions − [3, 1, 2, 4, 5] and [3, 1, 4, 2, 5]. Consequently, it is impossible to make three distinct sequences of tasks.