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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 2010-2021 Mike Mirzayanov

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