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, ... an. The i-th datatype have size ai bits, so it can represent every integer between 0 and 2ai - 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 ai bits) and x·x does not fit in some other type j (in aj bits) where ai < aj, 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 ≤ ai ≤ 109) — sizes of datatypes in bits. Some datatypes may have equal sizes.

Output

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

见题面 Input 部分

见题面 Output 部分

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