Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

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

B. Datatypes

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputTattah's youngest brother, Tuftuf, is new to programming.

Since his older brother is such a good programmer, his biggest dream is to outshine him. Tuftuf is a student at the German University in Cairo (GUC) where he learns to write programs in Gava.

Today, Tuftuf was introduced to Gava's unsigned integer datatypes. Gava has *n* unsigned integer datatypes of sizes (in bits) *a*_{1}, *a*_{2}, ... *a*_{n}. The *i*-th datatype have size *a*_{i} bits, so it can represent every integer between 0 and 2^{ai} - 1 inclusive.

Tuftuf is thinking of learning a better programming language. If there exists an integer *x*, such that *x* fits in some type *i* (in *a*_{i} bits) and *x*·*x* does not fit in some other type *j* (in *a*_{j} bits) where *a*_{i} < *a*_{j}, then Tuftuf will stop using Gava.

Your task is to determine Tuftuf's destiny.

Input

The first line contains integer *n* (2 ≤ *n* ≤ 10^{5}) — the number of Gava's unsigned integer datatypes' sizes. The second line contains a single-space-separated list of *n* integers (1 ≤ *a*_{i} ≤ 10^{9}) — sizes of datatypes in bits. Some datatypes may have equal sizes.

Output

Print "YES" if Tuftuf will stop using Gava, and "NO" otherwise.

Examples

Input

3

64 16 32

Output

NO

Input

4

4 2 1 3

Output

YES

Note

In the second example, *x* = 7 (111_{2}) fits in 3 bits, but *x*^{2} = 49 (110001_{2}) does not fit in 4 bits.

Codeforces (c) Copyright 2010-2017 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Apr/25/2017 13:36:34 (p1).

Desktop version, switch to mobile version.
User lists

Name |
---|