B. Datatypes
time limit per test
2 seconds
memory limit per test
256 megabytes
input
stdin
output
stdout

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.

Examples
Input
3
64 16 32
Output
NO
Input
4
4 2 1 3
Output
YES
Note

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