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.

Input

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.

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 $*p*_{*x*}$, 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 $*x*$.

Note

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