5 ;; N=5 manatees 1 2 3 4 5 1 2 3 4 5 5 4 1 2 3 0 ;; End of first test case 6 ;; N=6 manatees 1 2 3 4 5 6 6 5 4 3 2 1 0 ;; End of second test case 0 ;; No more test cases (The text in blue is commentary and will not be present in the inp

Given the desired order in which the manatees are to arrive down south, how do I dermine if there is any way Hugh can use the drainpipe to achive the desired order?

This problem can be solved by using a stack. A stack is an ordered collected of elements that operations to push(), peek(), pop(). In Java the interface Deque has those operations. The ArrayDeque class implements the Deque Interface.

Input

All input is to be read from the standard input stream.

The input consists of several blocks of lines and is terminated by a line with just 0.

The first line of each block indicates the number of manatees 0 < N < 100,000. In each of the next lines of the block there is a permutation of the numbers 1, 2, ..., N. For N=3, the permutation 2 3 1 means that the first manatee needs to be placed at the end of line and that the second manatee needs to be placed at the front of the line. The last line of each block contains just 0 signaling the end of the block.

Output

For each permutation in the input, the output is either the word "Yes" or "No" on a line by itself. See the sample below.

Sample Input

5 ;; N=5 manatees 1 2 3 4 5

1 2 3 4 5

5 4 1 2 3

0 ;; End of first test case

6 ;; N=6 manatees 1 2 3 4 5 6

6 5 4 3 2 1

0 ;; End of second test case

0 ;; No more test cases

(The text in blue is commentary and will not be present in the input.)

Sample Output

Yes ;; 1 2 3 4 5 <-- 1 2 3 4 5 is possible

No ;; 5 4 1 2 3 <-- 1 2 3 4 5 is NOT possible

Yes ;; 6 5 4 3 2 1 <-- 1 2 3 4 5 6 is possible

(The text in blue is commentary and must not appear in the output.)