A satellite's onboard log records the intervals of its orbit during which its solar panel is in direct sunlight, given as a list of [start, end] pairs sorted by start time, where no two intervals overlap (though two may touch end-to-end). Mission control has identified an eclipse interval [rs, re] during which the satellite passes into a planet's shadow and receives no sunlight, regardless of what the log says.

For every sunlight interval, remove whatever portion of it falls inside the eclipse interval: split the interval into two pieces if the eclipse cuts through its middle, shrink it if the eclipse only clips one end, leave it untouched if the eclipse doesn't reach it, or discard it entirely if the eclipse fully covers it. Report the resulting list of sunlight intervals, in order of start time, keeping only intervals with strictly positive length.

Input format

Line 1: an integer n — the number of sunlight intervals. Line 2: two integers rs and re — the eclipse interval. Each of the next n lines contains two integers s and e — one sunlight interval, in order of increasing s.

Output format

First line: an integer m — the number of resulting sunlight intervals. Each of the next m lines: two integers s and e, the resulting interval, in order of increasing s.

Constraints

• 0 <= n <= 10^5
• -10^9 <= s < e <= 10^9 for every input sunlight interval
• -10^9 <= rs < re <= 10^9
• The input sunlight intervals are sorted by s and pairwise non-overlapping (the next interval's s is >= the previous interval's e).

3
1 6
0 2
3 4
5 7

2
0 1
6 7

1
0 5
0 5

0