Datatypes

2000ms

262144K

Description:

Tattah'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) a₁, a₂, ... a_n. The i-th datatype have size a_i bits, so it can represent every integer between 0 and 2^a_i - 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 ≤ 10⁵) — the number of Gava's unsigned integer datatypes' sizes. The second line contains a single-space-separated list of n integers (1 ≤ a_i ≤ 10⁹) — sizes of datatypes in bits. Some datatypes may have equal sizes.

Output:

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

Sample Input:

3
64 16 32

Sample Output:

NO

Sample Input:

4
4 2 1 3

Sample Output:

YES

Note:

In the second example, x = 7 (111₂) fits in 3 bits, but x² = 49 (110001₂) does not fit in 4 bits.

Informação

Provedor Codeforces

Código CF108B