An equity research desk logs every coverage note as a pair: which analyst wrote it and which stock it covers. Two stocks are said to be linked by an analyst if that analyst has published a coverage note on both stocks. Given the complete list of coverage records, find the largest number of analysts that link any single pair of distinct stocks, then report every pair of stocks achieving this maximum overlap, along with the overlap count.

Input format

• Line 1: a single integer m, the number of coverage records.
• Each of the next m lines contains two integers, analyst_id and stock_id, meaning analyst analyst_id has published a coverage note on stock stock_id. The same (analyst_id, stock_id) pair never repeats in the input.

Output format

Let k be the maximum, over all pairs of distinct stock ids appearing in the input, of the number of distinct analyst ids covering both stocks in the pair (only pairs linked by at least one common analyst are considered). Print every pair of distinct stock ids (s1, s2) with s1 < s2 whose common-analyst count equals k, one pair per line, formatted as "s1 s2 k". Order the printed lines by s1 ascending, then by s2 ascending. It is guaranteed that at least one pair of stocks shares at least one common analyst.

Constraints

• 1 <= m <= 2000
• 1 <= analyst_id, stock_id <= 100000

6
1 10
1 20
1 30
2 10
2 20
3 30

10 20 2

8
1 5
1 6
2 5
2 6
3 7
3 8
4 7
4 8

5 6 2
7 8 2