A8200. Datatypes

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) $a_{1},a_{2},...\ a_{n}$ . The $i$ -th datatype have size $a_{i}$ bits, so it can represent every integer between $0$ and $2^{a_{i}}-1$ 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.

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.

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

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