B. Jeff and Periods
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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 ≤ 105). The next line contains integers a 1, a 2, ..., a n (1 ≤ a i ≤ 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 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.

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 p 2 = 0.