One day Jeff got hold of an integer sequence
a1,
a2,
...,
an 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 ai=x). These numbers, sorted in the increasing order, must form an arithmetic progression.
Help Jeff, find all
x that meet the problem conditions.
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
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.
Note
In the first test
2 occurs exactly once in the sequence, ergo
p2=0.