A9248. Jeff and Periods

One day Jeff got hold of an integer sequence $a_{1}$ , $a_{2}$ , $...$ , $a_{n}$ 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 $a_{i}=x$ ). These numbers, sorted in the increasing order, must form an arithmetic progression.

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

The first line contains integer $n$ $(1<=n<=10^{5})$ . The next line contains integers $a_{1}$ , $a_{2}$ , $...$ , $a_{n}$ $(1<=a_{i}<=10^{5})$ . The numbers are separated by spaces.

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

In the first test $2$ occurs exactly once in the sequence, ergo $p_{2}=0$ .