Mirko got a set of intervals for his birthday. There are many games he can play with them. In one of them, Mirko must find the longest sequence of distinct intervals such that each interval in the sequence is in the set and that each interval contains the one that follows in the sequence.
Write a program which finds one such longest sequence.
Input Specification
The first line of input contains the integer
, the number of intervals in the set.
Each of the following
lines contains two integers
and
describing one interval
.
Output Specification
Output the length of the longest sequence on the first line.
Each of the following
lines should contain one element of the sequence, an interval in the same
format it was given in the input.
Sample Input 1
3
3 4
2 5
1 6
Sample Output 1
3
1 6
2 5
3 4
Sample Input 2
5
10 30
20 40
30 50
10 60
30 40
Sample Output 2
3
10 60
30 50
30 40
Sample Input 3
6
1 4
1 5
1 6
1 7
2 5
3 5
Sample Output 3
5
1 7
1 6
1 5
2 5
3 5
DMOJ Editor's note
A sequence is an ordered list of elements. For example, is a sequence taken from elements of
.
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