You are given a sequence a_1, a_2, ..., a_n consisting of n integers.

You can choose any non-negative integer D (i.e. D ≥ 0), and for each a_i you can:

  * add D (only once), i. e. perform a_i := a_i + D, or 
  * subtract D (only once), i. e. perform a_i := a_i - D, or 
  * leave the value of a_i unchanged. 



It is possible that after an operation the value a_i becomes negative.

Your goal is to choose such minimum non-negative integer D and perform changes in such a way, that all a_i are equal (i.e. a_1=a_2=...=a_n).

Print the required D or, if it is impossible to choose such value D, print -1.

For example, for array [2, 8] the value D=3 is minimum possible because you can obtain the array [5, 5] if you will add D to 2 and subtract D from 8. And for array [1, 4, 7, 7] the value D=3 is also minimum possible. You can add it to 1 and subtract it from 7 and obtain the array [4, 4, 4, 4].

Input

The first line of the input contains one integer n (1 ≤ n ≤ 100) — the number of elements in a.

The second line of the input contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 100) — the sequence a.

Output

Print one integer — the minimum non-negative integer value D such that if you add this value to some a_i, subtract this value from some a_i and leave some a_i without changes, all obtained values become equal.

If it is impossible to choose such value D, print -1.

Examples

Input


6
1 4 4 7 4 1


Output


3


Input


5
2 2 5 2 5


Output


3


Input


4
1 3 3 7


Output


-1


Input


2
2 8


Output


3
//package codeforces552;

import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.HashSet;
import java.util.InputMismatchException;
import java.util.Set;

public class B {
  InputStream is;
  PrintWriter out;
  String INPUT = "2\n" +
      "1 1";
  String INPUTB = "6\n" +
      "1 4 4 7 4 1";

  void solve() {
    int n = ni();
    int[] a = na(n);
    int ans = 10000;
    if (n == 1) {
      out.println(0);
      return;
    }
    for (int x = -100; x <= 100; x++) {
      int d = -1000;
      boolean ok = true;
      for (int j = 0; j < n; j++) {
        if (a[j] == x) {
        } else {
          if (d == -1000) {
            d = Math.abs(a[j] - x);
          } else if (Math.abs(a[j] - x) == d) {
          } else {
            ok = false;
            break;
          }
        }
      }
      if (d == -1000) {
        d = 0;
      }
      if (ok) {
        ans = Math.min(ans, d);
      }
    }
    if (ans == 10000) {
      out.println(-1);
    } else {
      out.println(ans);
    }
  }


  void run() throws Exception {
    is = oj ? System.in : new ByteArrayInputStream(INPUT.getBytes());
    out = new PrintWriter(System.out);

    long s = System.currentTimeMillis();
    solve();
    out.flush();
    tr(System.currentTimeMillis() - s + "ms");
  }

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

  private byte[] inbuf = new byte[1024];
  public int lenbuf = 0, ptrbuf = 0;

  private int readByte() {
    if (lenbuf == -1) throw new InputMismatchException();
    if (ptrbuf >= lenbuf) {
      ptrbuf = 0;
      try {
        lenbuf = is.read(inbuf);
      } catch (IOException e) {
        throw new InputMismatchException();
      }
      if (lenbuf <= 0) return -1;
    }
    return inbuf[ptrbuf++];
  }

  private boolean isSpaceChar(int c) {
    return !(c >= 33 && c <= 126);
  }

  private int skip() {
    int b;
    while ((b = readByte()) != -1 && isSpaceChar(b)) ;
    return b;
  }

  private double nd() {
    return Double.parseDouble(ns());
  }

  private char nc() {
    return (char) skip();
  }

  private String ns() {
    int b = skip();
    StringBuilder sb = new StringBuilder();
    while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != ' ')
      sb.appendCodePoint(b);
      b = readByte();
    }
    return sb.toString();
  }

  private char[] ns(int n) {
    char[] buf = new char[n];
    int b = skip(), p = 0;
    while (p < n && !(isSpaceChar(b))) {
      buf[p++] = (char) b;
      b = readByte();
    }
    return n == p ? buf : Arrays.copyOf(buf, p);
  }

  private char[][] nm(int n, int m) {
    char[][] map = new char[n][];
    for (int i = 0; i < n; i++) map[i] = ns(m);
    return map;
  }

  private int[] na(int n) {
    int[] a = new int[n];
    for (int i = 0; i < n; i++) a[i] = ni();
    return a;
  }

  private int ni() {
    int num = 0, b;
    boolean minus = false;
    while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
    if (b == '-') {
      minus = true;
      b = readByte();
    }

    while (true) {
      if (b >= '0' && b <= '9') {
        num = num * 10 + (b - '0');
      } else {
        return minus ? -num : num;
      }
      b = readByte();
    }
  }

  private long nl() {
    long num = 0;
    int b;
    boolean minus = false;
    while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
    if (b == '-') {
      minus = true;
      b = readByte();
    }

    while (true) {
      if (b >= '0' && b <= '9') {
        num = num * 10 + (b - '0');
      } else {
        return minus ? -num : num;
      }
      b = readByte();
    }
  }

  private boolean oj = true;

  private void tr(Object... o) {
    if (!oj) System.out.println(Arrays.deepToString(o));
  }
}