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.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.StringTokenizer;

public class Jeff_and_Periods_352 {

	public static void main(String[] args) throws IOException {
		Jeff_and_Periods_352 main = new Jeff_and_Periods_352();
		main.input();
		main.solve();

	}

	private void solve() {
		StringBuilder res = new StringBuilder();
		int cRes = 0;
		for (int i = minPos; i <= maxPos; i++) {
			if (val[i] >= 0) {
				res.append(i + " " + val[i] + "\n");
				cRes++;
			}
		}
		System.out.println(cRes);
		System.out.println(res);
	}

	/******************************************************************
	 ****************************** INPUT******************************
	 ******************************************************************/

	static int n;
	static int[] a;
	static int[] val = new int[100001];
	static int[] pos = new int[100001];
	static int minPos = 0;
	static int maxPos = 0;

	void input() throws IOException {
		Init(System.in);
		n = NextInt();
		a = new int[n];
		int numb = 0;

		Arrays.fill(val, -1);
		Arrays.fill(pos, -1);
		for (int i = 0; i < n; i++) {
			numb = NextInt();
			minPos = Math.min(minPos, numb);
			maxPos = Math.max(maxPos, numb);
			if (val[numb] == -1) {
				val[numb] = 0;
				pos[numb] = i;
			} else if (val[numb] == 0) {
				val[numb] = i - pos[numb];
				pos[numb] = i;
			} else {
				if (i - pos[numb] == val[numb]) {
					pos[numb] = i;
				} else {
					val[numb] = Integer.MIN_VALUE;
				}
			}
		}
	}

	/******************************************************************
	 ****************************** READER*****************************
	 ******************************************************************/
	static BufferedReader reader;
	static StringTokenizer tokenizer;

	static void Init(InputStream input) {
		reader = new BufferedReader(new InputStreamReader(input));
		tokenizer = new StringTokenizer("");
	}

	static String Next() throws IOException {

		while (!tokenizer.hasMoreTokens()) {
			tokenizer = new StringTokenizer(reader.readLine());
		}
		return tokenizer.nextToken();
	}

	static int NextInt() throws IOException {

		return Integer.parseInt(Next());
	}

	static long NextLong() throws IOException {

		return Long.parseLong(Next());
	}

	static Double NextDouble() throws IOException {

		return Double.parseDouble(Next());
	}
}
