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 Main { 
    public static void main(String[] args) { 
        InputStream input = System.in;
        OutputStream output = System.out;
        InputReader in = new InputReader(input);
        PrintWriter out = new PrintWriter(output);
        Solution s = new Solution();
        s.solve(1, in, out);
        out.close();
    }

    static class Solution { 
        
        double EPS = 0.0000001;
        public void solve(int cs, InputReader in, PrintWriter out) {
            int n = in.nextInt(), counts = 0;
            E[] arr = new E[100001];
            for (int i = 0; i < n; ++i) {
                int x = in.nextInt();
                E e = null;
                if (arr[x] == null) {
                    e = new E();
                    e.last = i;
                    e.count++;
                    arr[x] = e;
                    counts++;
                }
                else {
                    if (arr[x].count == 1) {
                        arr[x].diff = i-arr[x].last;
                        arr[x].last = i;
                        arr[x].count++;
                    }
                    else if (arr[x].count >= 2) {
                        int dd = i - arr[x].last;
                        if (dd == arr[x].diff) {
                            arr[x].count++;
                        } else {
                            arr[x].count = -1;
                            counts--;
                        }
                        arr[x].last = i;
                    }
                }

            }
            out.println(counts);
            for (int i = 0; i < arr.length; ++i) {
                if (arr[i] != null && arr[i].count >= 0) {
                    out.println(i + " " + arr[i].diff);
                }
            }
        }

        static class E {
            int count, diff, last;

        }
    }

    static class InputReader { 
        BufferedReader br;
        StringTokenizer st;
        
        public InputReader(InputStream i) {
            br = new BufferedReader(new InputStreamReader(i), 32768);
            st = null;
        }

        public InputReader(FileReader s) {
            br = new BufferedReader(s);
            st = null;
        }

        public String next() {
            while (st == null || !st.hasMoreTokens()) {
                try { 
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return st.nextToken();
        }

        public int nextInt() { 
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public String nextLine() { 
            try { 
                return br.readLine();
            } catch (IOException e) { 
                throw new RuntimeException(e);
            }
        }
    }
    static class Reader {
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;
        public Reader(){
            din=new DataInputStream(System.in);
            buffer=new byte[BUFFER_SIZE];
            bufferPointer=bytesRead=0;
        }

        public Reader(String file_name) throws IOException{
            din=new DataInputStream(new FileInputStream(file_name));
            buffer=new byte[BUFFER_SIZE];
            bufferPointer=bytesRead=0;
        }

        public String readLine() throws IOException{
            byte[] buf=new byte[64]; // line length
            int cnt=0,c;
            while((c=read())!=-1){
                if(c=='\n')break;
                buf[cnt++]=(byte)c;
            }
            return new String(buf,0,cnt);
        }

        public int nextInt() throws IOException{
            int ret=0;byte c=read();
            while(c<=' ')c=read();
            boolean neg=(c=='-');
            if(neg)c=read();
            do{ret=ret*10+c-'0';}while((c=read())>='0'&&c<='9');
            if(neg)return -ret;
            return ret;
        }

        public long nextLong() throws IOException{
            long ret=0;byte c=read();
            while(c<=' ')c=read();
            boolean neg=(c=='-');
            if(neg)c=read();
            do{ret=ret*10+c-'0';}while((c=read())>='0'&&c<='9');
            if(neg)return -ret;
            return ret;
        }

        public double nextDouble() throws IOException{
            double ret=0,div=1;byte c=read();
            while(c<=' ')c=read();
            boolean neg=(c=='-');
            if(neg)c = read();
            do {ret=ret*10+c-'0';}while((c=read())>='0'&&c<='9');
            if(c=='.')while((c=read())>='0'&&c<='9')
                ret+=(c-'0')/(div*=10);
            if(neg)return -ret;
            return ret;
        }

        private void fillBuffer() throws IOException{
            bytesRead=din.read(buffer,bufferPointer=0,BUFFER_SIZE);
            if(bytesRead==-1)buffer[0]=-1;
        }

        private byte read() throws IOException{
            if(bufferPointer==bytesRead)fillBuffer();
            return buffer[bufferPointer++];
        }

        public void close() throws IOException{
            if(din==null) return;
            din.close();
        }
    }
}


