There are N cats. We number them from 1 through N.

Each of the cats wears a hat. Cat i says: "there are exactly a_i different colors among the N - 1 hats worn by the cats except me."

Determine whether there exists a sequence of colors of the hats that is consistent with the remarks of the cats.

Constraints

* 2 ≤ N ≤ 10^5
* 1 ≤ a_i ≤ N-1

Input

Input is given from Standard Input in the following format:


N
a_1 a_2 ... a_N


Output

Print `Yes` if there exists a sequence of colors of the hats that is consistent with the remarks of the cats; print `No` otherwise.

Examples

Input

3
1 2 2


Output

Yes


Input

3
1 1 2


Output

No


Input

5
4 3 4 3 4


Output

No


Input

3
2 2 2


Output

Yes


Input

4
2 2 2 2


Output

Yes


Input

5
3 3 3 3 3


Output

No
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.util.stream.IntStream;
import java.util.Arrays;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.OptionalInt;
import java.io.BufferedOutputStream;
import java.io.UncheckedIOException;
import java.nio.charset.Charset;
import java.util.StringTokenizer;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.BufferedReader;
import java.util.NoSuchElementException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author mikit
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        LightScanner in = new LightScanner(inputStream);
        LightWriter out = new LightWriter(outputStream);
        BColorfulHats solver = new BColorfulHats();
        solver.solve(1, in, out);
        out.close();
    }

    static class BColorfulHats {
        public void solve(int testNumber, LightScanner in, LightWriter out) {
            // out.setBoolLabel(LightWriter.BoolLabel.YES_NO_FIRST_UP);
            int n = in.ints();
            int[] a = in.ints(n);
            int max = IntMath.max(a), min = IntMath.min(a);
            if (max - min > 1) {
                out.noln();
                return;
            } else if (max == min) {
                out.ans(min * 2 <= n || min == n - 1).ln();
                return;
            }
            int uniq = 0;
            for (int i = 0; i < n; i++) if (a[i] == min) uniq++;
            int s = max - uniq, t = n - uniq;
            out.ans(uniq + 1 <= max && s * 2 <= t).ln();
        }

    }

    static class LightScanner {
        private BufferedReader reader = null;
        private StringTokenizer tokenizer = null;

        public LightScanner(InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
        }

        public String string() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new UncheckedIOException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int ints() {
            return Integer.parseInt(string());
        }

        public int[] ints(int length) {
            return IntStream.range(0, length).map(x -> ints()).toArray();
        }

    }

    static class LightWriter implements AutoCloseable {
        private final Writer out;
        private boolean autoflush = false;
        private boolean breaked = true;
        private LightWriter.BoolLabel boolLabel = LightWriter.BoolLabel.YES_NO_FIRST_UP;

        public LightWriter(Writer out) {
            this.out = out;
        }

        public LightWriter(OutputStream out) {
            this(new OutputStreamWriter(new BufferedOutputStream(out), Charset.defaultCharset()));
        }

        public LightWriter print(char c) {
            try {
                out.write(c);
                breaked = false;
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
            return this;
        }

        public LightWriter print(String s) {
            try {
                out.write(s, 0, s.length());
                breaked = false;
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
            return this;
        }

        public LightWriter ans(String s) {
            if (!breaked) {
                print(' ');
            }
            return print(s);
        }

        public LightWriter ans(boolean b) {
            return ans(boolLabel.transfer(b));
        }

        public LightWriter noln() {
            return ans(false).ln();
        }

        public LightWriter ln() {
            print(System.lineSeparator());
            breaked = true;
            if (autoflush) {
                try {
                    out.flush();
                } catch (IOException ex) {
                    throw new UncheckedIOException(ex);
                }
            }
            return this;
        }

        public void close() {
            try {
                out.close();
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
        }

        public enum BoolLabel {
            YES_NO_FIRST_UP("Yes", "No"),
            YES_NO_ALL_UP("YES", "NO"),
            YES_NO_ALL_DOWN("yes", "no"),
            Y_N_ALL_UP("Y", "N"),
            POSSIBLE_IMPOSSIBLE_FIRST_UP("Possible", "Impossible"),
            POSSIBLE_IMPOSSIBLE_ALL_UP("POSSIBLE", "IMPOSSIBLE"),
            POSSIBLE_IMPOSSIBLE_ALL_DOWN("possible", "impossible"),
            FIRST_SECOND_FIRST_UP("First", "Second"),
            FIRST_SECOND_ALL_UP("FIRST", "SECOND"),
            FIRST_SECOND_ALL_DOWN("first", "second"),
            ALICE_BOB_FIRST_UP("Alice", "Bob"),
            ALICE_BOB_ALL_UP("ALICE", "BOB"),
            ALICE_BOB_ALL_DOWN("alice", "bob"),
            ;
            private final String positive;
            private final String negative;

            BoolLabel(String positive, String negative) {
                this.positive = positive;
                this.negative = negative;
            }

            private String transfer(boolean f) {
                return f ? positive : negative;
            }

        }

    }

    static final class IntMath {
        private IntMath() {
        }

        public static int min(int... v) {
            return Arrays.stream(v).min().orElseThrow(NoSuchElementException::new);
        }

        public static int max(int... v) {
            return Arrays.stream(v).max().orElseThrow(NoSuchElementException::new);
        }

    }
}

