One day Jeff got hold of an integer sequence a1, a2, ..., an of length n. The boy immediately decided to analyze the sequence. For that, he needs to find all values of x, for which these conditions hold:

  * x occurs in sequence a. 
  * Consider all positions of numbers x in the sequence a (such i, that ai = x). These numbers, sorted in the increasing order, must form an arithmetic progression. 



Help Jeff, find all x that meet the problem conditions.

Input

The first line contains integer n (1 ≤ n ≤ 105). The next line contains integers a1, a2, ..., an (1 ≤ ai ≤ 105). The numbers are separated by spaces.

Output

In the first line print integer t — the number of valid x. On each of the next t lines print two integers x and px, where x is current suitable value, px is the common difference between numbers in the progression (if x occurs exactly once in the sequence, px must equal 0). Print the pairs in the order of increasing x.

Examples

Input

1
2


Output

1
2 0


Input

8
1 2 1 3 1 2 1 5


Output

4
1 2
2 4
3 0
5 0

Note

In the first test 2 occurs exactly once in the sequence, ergo p2 = 0.

import java.io.*;
import java.util.*;


public class Codeforces {


    public static void main(String[] args) throws IOException {
        Reader.init(System.in);
        int n = Reader.nextInt();
        
        Num arr[] = new Num[100001];
        
        for(int i = 0; i < n; i++){
            int x = Reader.nextInt();
            
            if(arr[x] == null)
                arr[x] = new Num(i, 0, true);
            
            else if(arr[x].diff == 0){
                arr[x].diff = i - arr[x].lastIndex;
                arr[x].lastIndex = i;
            }
            
            else if(arr[x].b){
                
                if(i - arr[x].lastIndex != arr[x].diff)
                    arr[x].b = false;
                
                arr[x].lastIndex = i;
            }
        }
        
        StringBuilder ans = new StringBuilder();
        int count = 0;
        
        for(int i = 1; i < 100001; i++){
            
            if(arr[i] != null && arr[i].b){
                ans.append(i).append(" ").append(arr[i].diff).append("\n");
                count++;
            }
        }
        
        System.out.print(count + "\n" + ans);
    }
}

class Num{
    int lastIndex;
    int diff;
    boolean b;
    
    public Num(int lastIndex, int diff, boolean b){
        this.b = b;
        this.diff = diff;
        this.lastIndex = lastIndex;
    }
}

class Reader {

    static BufferedReader reader;
    static StringTokenizer tokenizer;

    /**
     * call this method to initialize reader for InputStream
     */
    static void init(InputStream input) {
        reader = new BufferedReader(
                new InputStreamReader(input));
        tokenizer = new StringTokenizer("");
    }

    /**
     * get next word
     */
    static String next() throws IOException {
        while (!tokenizer.hasMoreTokens()) {
            //TODO add check for eof if necessary
            tokenizer = new StringTokenizer(
                    reader.readLine());
        }
        return tokenizer.nextToken();
    }

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

    static byte nextByte() throws IOException {
        return Byte.parseByte(next());
    }

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

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