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:
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.
1
2
1
2 0
8
1 2 1 3 1 2 1 5
4
1 2
2 4
3 0
5 0
In the first test 2 occurs exactly once in the sequence, ergo p _{2} = 0.
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