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.
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.
Print "YES" if Tuftuf will stop using Gava, and "NO" otherwise.
3
64 16 32
NO
4
4 2 1 3
YES
In the second example, x=7 (1112) fits in 3 bits, but x2=49 (1100012) does not fit in 4 bits.