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.
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.StringTokenizer;

/**
 * Date 25.11.2011
 * Time 20:43:22
 * Author Woodey
 * $
 */

public class B108 {
	
	final int INF = Integer.MAX_VALUE;
	
	private void Solution() throws IOException {
		int n = nextInt();
		int[] mas = new int[n];
		boolean win = false;
		for (int i = 0; i < n; i ++)
			mas[i] = nextInt();
		Arrays.sort(mas);
		for (int i = 0; i < n-1; i ++)
			if (mas[i]*2 > mas[i+1] && mas[i] != mas[i+1])
				win = true;
		System.out.println(win ? "YES" : "NO");
	}

	public static void main(String[] args) {
		new B108().run();
	}

	BufferedReader in;
	StringTokenizer tokenizer;

	public void run() {
		try {
			in = new BufferedReader(new InputStreamReader(System.in));
			tokenizer = null;
			Solution();
			in.close();
		} catch (Exception e) {
			e.printStackTrace();
			System.exit(1);
		}
	}

	int nextInt() throws IOException {
		return Integer.parseInt(nextToken());
	}

	String nextToken() throws IOException {
		while (tokenizer == null || !tokenizer.hasMoreTokens())
			tokenizer = new StringTokenizer(in.readLine());
		return tokenizer.nextToken();
	}
}
