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.

输入描述:

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.

输出描述:

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.

备注:

In the first test 2 occurs exactly once in the sequence, ergo p2 = 0.