One day Anna got the following task at school: to arrange several numbers in a circle so that any two neighboring numbers differs exactly by 1. Anna was given several numbers and arranged them in a circle to fulfill the task. Then she wanted to check if she had arranged the numbers correctly, but at this point her younger sister Maria came and shuffled all numbers. Anna got sick with anger but what's done is done and the results of her work had been destroyed. But please tell Anna: could she have hypothetically completed the task using all those given numbers?

Input

The first line contains an integer n — how many numbers Anna had (3 ≤ n ≤ 105). The next line contains those numbers, separated by a space. All numbers are integers and belong to the range from 1 to 109.

Output

Print the single line "YES" (without the quotes), if Anna could have completed the task correctly using all those numbers (using all of them is necessary). If Anna couldn't have fulfilled the task, no matter how hard she would try, print "NO" (without the quotes).

Examples

Input

4
1 2 3 2


Output

YES


Input

6
1 1 2 2 2 3


Output

YES


Input

6
2 4 1 1 2 2


Output

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

//created at 10:14 AM 11/15/11 by Abrackadabra

public class D {
    int IOMode = 0; //0 - consoleIO, 1 - <taskName>.in/out, 2 - input.txt/output.txt, 3 - test case generator
    String taskName = "";

    void solve() throws IOException {
        int n = nextInt();
        int[] a = new int[n];
        TreeMap<Integer, Integer> have = new TreeMap<Integer, Integer>();
        for (int i = 0; i < n; i++) {
            a[i] = nextInt();
            have.put(a[i], have.containsKey(a[i]) ? have.get(a[i]) + 1 : 1);
        }
        Arrays.sort(a);
        int l = a[0], r = a[0];
        have.put(a[0], have.get(a[0]) - 1);
        for (int i = 1; i < n; i++) {
            if (i % 2 == 1) {
                if (have.containsKey(l - 1) && have.get(l - 1) > 0) {
                    l--;
                    have.put(l, have.get(l) - 1);
                    continue;
                }
                if (have.containsKey(l + 1) && have.get(l + 1) > 0) {
                    l++;
                    have.put(l, have.get(l) - 1);
                    continue;
                }
                out.println("NO");
                return;
            } else {
                if (have.containsKey(r - 1) && have.get(r - 1) > 0) {
                    r--;
                    have.put(r, have.get(r) - 1);
                    continue;
                }
                if (have.containsKey(r + 1) && have.get(r + 1) > 0) {
                    r++;
                    have.put(r, have.get(r) - 1);
                    continue;
                }
                out.println("NO");
                return;
            }
        }
        if (Math.abs(l - r) == 1) {
            out.println("YES");
        } else {
            out.println("NO");
        }
    }

    public static void main(String[] args) throws IOException {
        if (args.length > 0 && args[0].equals("Abra")) debugMode = true;
        new D().run();
    }

    long startTime = System.nanoTime(), tempTime = startTime, finishTime = startTime;
    long startMem = Runtime.getRuntime().totalMemory(), finishMem = startMem;

    void run() throws IOException {
        init();
        if (debugMode) {
            con.println("Start");
            con.println("Console output:");
        }
        solve();
        finishTime = System.nanoTime();
        finishMem = Runtime.getRuntime().totalMemory();
        out.flush();
        if (debugMode) {
            int maxSymbols = 1000, c = 0;
            BufferedReader tbr = new BufferedReader(new FileReader("input.txt"));
            char[] a = new char[maxSymbols];
            tbr.read(a);
            if (a[0] != 0) {
                con.println();
                con.println("File input:");
                con.print(a);
            }
            boolean left = true;
            for (int i = 0; i < maxSymbols; i++) left = left && a[i] != 0;
            if (left) con.println("...");
            else con.println();
            tbr = new BufferedReader(new FileReader("output.txt"));
            a = new char[maxSymbols];
            tbr.read(a);
            if (a[0] != 0) {
                con.println();
                con.println("File output:");
                con.print(a);
            }
            left = true;
            for (int i = 0; i < maxSymbols; i++) left = left && a[i] != 0;
            if (left) con.println("...");
            else con.println();
            con.println("Time passed:  " + (finishTime - startTime) / 1000000000.0 + " sec");
            con.println("Memory used:  " + (finishMem - startMem) + " bytes");
            con.println("Total memory: " + Runtime.getRuntime().totalMemory() + " bytes");
        }
    }

    boolean tick(double x) {
        if (System.nanoTime() - tempTime > x) {
            tempTime = System.nanoTime();
            con.println("Tick at " + (tempTime - startTime) / 1000000000 + " sec");
            con.print("   ");
            return true;
        }
        return false;
    }

    void printTime() {
        con.println((System.nanoTime() - tempTime) + " nanos passed");
        tempTime = System.nanoTime();
    }

    static boolean debugMode = false;
    PrintStream con = System.out;

    void init() throws IOException {
        if (debugMode && IOMode != 3) {
            br = new BufferedReader(new FileReader("input.txt"));
            out = new PrintWriter(new FileWriter("output.txt"));
        } else
            switch (IOMode) {
                case 0:
                    br = new BufferedReader(new InputStreamReader(System.in));
                    out = new PrintWriter(System.out);
                    break;
                case 1:
                    br = new BufferedReader(new FileReader(taskName + ".in"));
                    out = new PrintWriter(new FileWriter(taskName + ".out"));
                    break;
                case 2:
                    br = new BufferedReader(new FileReader("input.txt"));
                    out = new PrintWriter(new FileWriter("output.txt"));
                    break;
                case 3:
                    out = new PrintWriter(new FileWriter("input.txt"));
                    break;
            }
    }

    BufferedReader br;
    PrintWriter out;
    StringTokenizer in;

    boolean hasMoreTokens() throws IOException {
        while (in == null || !in.hasMoreTokens()) {
            String line = br.readLine();
            if (line == null) return false;
            in = new StringTokenizer(line);
        }
        return true;
    }

    String nextString() throws IOException {
        return hasMoreTokens() ? in.nextToken() : null;
    }

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

    long nextLong() throws IOException {
        return Long.parseLong(nextString());
    }

    double nextDouble() throws IOException {
        return Double.parseDouble(nextString());
    }
}
