Iahub and Iahubina went to a picnic in a forest full of trees. Less than 5 minutes passed before Iahub remembered of trees from programming. Moreover, he invented a new problem and Iahubina has to solve it, otherwise Iahub won't give her the food. 

Iahub asks Iahubina: can you build a rooted tree, such that

  * each internal node (a node with at least one son) has at least two sons; 
  * node i has ci nodes in its subtree? 



Iahubina has to guess the tree. Being a smart girl, she realized that it's possible no tree can follow Iahub's restrictions. In this way, Iahub will eat all the food. You need to help Iahubina: determine if there's at least one tree following Iahub's restrictions. The required tree must contain n nodes.

Input

The first line of the input contains integer n (1 ≤ n ≤ 24). Next line contains n positive integers: the i-th number represents ci (1 ≤ ci ≤ n).

Output

Output on the first line "YES" (without quotes) if there exist at least one tree following Iahub's restrictions, otherwise output "NO" (without quotes). 

Examples

Input

4
1 1 1 4


Output

YES

Input

5
1 1 5 2 1


Output

NO
import java.util.*;
import java.io.*;
import java.math.*;
import java.awt.geom.*;

import static java.lang.Math.*;

public class Solution implements Runnable {
    
    int n;
    int[] c;
    int[] deg;
    int sum = 0;
    
    boolean backtrack(int pos) {
        if (pos == n) {
            return sum == 0;
        }
        if (pos == 0) {
            c[pos]--;
            sum--;
            if (backtrack(pos + 1)) {
                return true;
            }
            c[pos]++;
            sum++;
        } else {
            boolean good = true;
            for (int i = 0; i < pos && good; i++) {
                if (c[i] >= c[pos]) {
                    c[i] -= c[pos];
                    sum -= c[pos];
                    deg[i]++;
                    if (deg[i] > 1 || c[i] > 0) {
                        c[pos]--;
                        sum--;
                        if (backtrack(pos + 1)) {
                            return true;
                        }
                        c[pos]++;
                        sum++;
                        if (c[pos] == 1) {
                            good = false;
                        }
                    }
                    deg[i]--;
                    c[i] += c[pos];
                    sum += c[pos];
                }
            }
        }
        return false;
    }
    
    public void solve() throws Exception {
        n = sc.nextInt();
        c = new int[n];
        deg = new int[n];
        int ones = 0;
        for (int i = 0; i < n; i++) {
            c[i] = -sc.nextInt();
        }
        Arrays.sort(c);
        for (int i = 0; i < n; i++) {
            c[i] = -c[i];
            sum += c[i];
            if (c[i] == 1) {
                ones++;
            }
        }
        if (ones * 2 < n) {
            out.println("NO");
            return;
        }
        if (backtrack(0)) {
            out.println("YES");
        } else {
            out.println("NO");
        }
    }

    static Throwable uncaught;

    BufferedReader in;
    FastScanner sc;
    PrintWriter out;

    @Override
    public void run() {
        try {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
            sc = new FastScanner(in);
            solve();
        } catch (Throwable uncaught) {
            Solution.uncaught = uncaught;
        } finally {
            out.close();
        }
    }

    public static void main(String[] args) throws Throwable {
        Thread thread = new Thread(null, new Solution(), "", (1 << 26));
        thread.start();
        thread.join();
        if (Solution.uncaught != null) {
            throw Solution.uncaught;
        }
    }

}

class FastScanner {

    BufferedReader in;
    StringTokenizer st;

    public FastScanner(BufferedReader in) {
        this.in = in;
    }

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

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

    public long nextLong() throws Exception {
        return Long.parseLong(nextToken());
    }

    public double nextDouble() throws Exception {
        return Double.parseDouble(nextToken());
    }

}