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.

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.

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.