Nissy likes Arithmetic Progression. He sees an array of integers $a_1, a_2, ..., a_n$ of length $n$. He wants to find all values of $x$ satisfying these conditions:

• $x$ occurs in the array

• Consider the positions/indices of occurrence of number $x$ in the array and on sorting these positions/indices in the ascending order, they must form an arithmetic progression.

But Nissy can’t find them all on his own. He needs your help in finding them.

Input Format:

First Line: An integer $n$

The next line contains integers $a_1, a_2, ..., a_n$  separated by spaces.

Output Format:

In the first line print an integer $t$ = the total number of valid $x$.

On each of the next $t$ lines print two space-separated integers $x$  and $dx$, where $x$ is the value and $dx$ is the common difference between the positions/indices of occurrences in the progression(if $x$ occurs exactly once in the sequence, $dx$ must equal 0). Print the pairs in the order of increasing $x$.

Constraints:

$1 \le n \le 10^5$

$1 \le a_i \le 10^5$