Social Distance

Limits: 2 sec., 256 MiB

This statement was translated automatically from Ukrainian.

People are standing in a queue to a store. The queue can be represented as a coordinate line. The \(i\)-th person is standing at coordinate \(x_i\).

As you know, in the middle of the COVID-19 pandemic, it is necessary to maintain social distance.

You need to tell whether the distance between every pair of people is at least 2 meters.

Input

The first line contains an integer \(n\) — the number of people in the queue.

The second line contains \(n\) integers — the coordinates of the people in the queue in meters, in order from left to right.

Output

In a single line, print YES if the people maintain the distance, and NO otherwise.

Constraints

\(1 \le n \le 10^4\),

\(0 \le x_i \le 10^9\),

\(x_i \le x_{i+1}\),

for 40% of the tests, an additional constraint \(n \le 100\) is satisfied.

Samples