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.

输入描述:

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.

输出描述:

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

备注:

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