The New Year is coming soon and Santa Claus has already started preparing his magical reindeer team, on which he delivers gifts to children. It is known that the team is driven by several magical deer, each of which is ridden by two elves.
But the magical deer – obstinate animals, so not any two elves can ride any deer. Namely, each deer is characterized by some obstinacy a
i, and each elf – temperament b
i. Two elves j and k can ride the i-th reindeer if and only if either b
j < a
i < b
k or b
k < a
i < b
j.
To make his appearance as spectacular as possible, Santa Claus wants his team to have as many reindeer as possible. About every deer Santa knows his obstinacy, and about every elf – his temperament.
Help Santa figure out the maximum number of reindeer he can include in his team, which reindeer he should choose, and which elves should ride them.
Input
The first line contains two integers m and n – the number of deer and elves, respectively ( 1 ≤ m, n ≤ 100,000).
The second line contains m integers ai – deer obstinacy ( 0 ≤ a
i ≤ 10
9). The third line contains n integers bi – elves temperament ( 0 ≤ b
i ≤ 10
9).
Imprint
In the first line print a single number k – the maximum number of reindeer that Santa Claus can include in his team. In the next k lines print three integers each: d
i, e
i, 1, e
i, 2 – for each reindeer in the team print its number and the numbers of the elves that will ride it. If there are several solutions, print any one.
Both elves and deer are numbered, starting from one, in the order in which they are given in the input.
Examples
| # |
Input |
Output |
| 1 |
4 6
2 3 4 5
1 3 2 2 5 2
| 2
1 1 2
3 4 5
|