Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

C. Ravioli Sort

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputEverybody knows of spaghetti sort. You decided to implement an analog sorting algorithm yourself, but as you survey your pantry you realize you're out of spaghetti! The only type of pasta you have is ravioli, but you are not going to let this stop you...

You come up with the following algorithm. For each number in the array *a*_{i}, build a stack of *a*_{i} ravioli. The image shows the stack for *a*_{i} = 4.

Arrange the stacks in one row in the order in which the corresponding numbers appear in the input array. Find the tallest one (if there are several stacks of maximal height, use the leftmost one). Remove it and add its height to the end of the output array. Shift the stacks in the row so that there is no gap between them. Repeat the procedure until all stacks have been removed.

At first you are very happy with your algorithm, but as you try it on more inputs you realize that it doesn't always produce the right sorted array. Turns out when two stacks of ravioli are next to each other (at any step of the process) and differ in height by two or more, the top ravioli of the taller stack slides down on top of the lower stack.

Given an input array, figure out whether the described algorithm will sort it correctly.

Input

The first line of input contains a single number *n* (1 ≤ *n* ≤ 10) — the size of the array.

The second line of input contains *n* space-separated integers *a*_{i} (1 ≤ *a*_{i} ≤ 100) — the elements of the array.

Output

Output "YES" if the array can be sorted using the described procedure and "NO" if it can not.

Examples

Input

3

1 2 3

Output

YES

Input

3

3 1 2

Output

NO

Note

In the second example the array will change even before the tallest stack is chosen for the first time: ravioli from stack of height 3 will slide on the stack of height 1, and the algorithm will output an array {2, 2, 2}.

Codeforces (c) Copyright 2010-2018 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Apr/22/2018 11:27:06 (d3).

Desktop version, switch to mobile version.

User lists

Name |
---|