Oh those picky $N$ ($1 \leq N \leq 50,000$) cows! They are so picky that each one will only be milked over some precise time interval $A..B$ ($1 \leq A \leq B \leq 1,000,000$), which includes both times $A$ and $B$. Obviously, FJ must create a reservation system to determine which stall each cow can be assigned for her milking time. Of course, no cow will share such a private moment with other cows.

Help FJ by determining: The minimum number of stalls required in the barn so that each cow can have her private milking period. An assignment of cows to these stalls over time. Many answers are correct for each test dataset; a program will grade your answer.

约翰的 $N$（$1\leq N\leq 50000$）头奶牛实在是太难伺候了，她们甚至有自己独特的产奶时段。对于某一头奶牛，她每天的产奶时段是固定的时间段 $[A,B]$（即 $A$ 到 $B$，包括 $A$ 和 $B$）。这使得约翰必须开发一个调控系统来决定每头奶牛应该被安排到哪个牛棚去挤奶，因为奶牛们并不希望在挤奶时被其它奶牛看见。

请帮约翰计算：如果要满足奶牛们的要求，并且每天每头奶牛都要被挤过奶，至少需要多少牛棚和每头牛应该在哪个牛棚被挤奶。如果有多种答案，输出任意一种均可。

Line $1$: A single integer, $N$

Lines $2..N+1$: Line $i+1$ describes cow $i$'s milking interval with two space-separated integers.

第 $1$ 行为一个整数 $N$。

第 $2\sim (N+1)$ 行，每行两个数字，第 $(i+1)$ 行的数字代表第 $i$ 头奶牛的产奶时段。

Line $1$: The minimum number of stalls the barn must have.

Lines $2..N+1$: Line $i+1$ describes the stall to which cow i will be assigned for her milking period.

第 $1$ 行输出一个整数，代表需要牛棚的最少数量。

第 $2\sim (N+1)$ 行，每行一个数字，第 $(i+1)$ 行的数字代表第 $i$ 头奶牛将会被安排到哪个牛棚挤奶。

4
1
2
3
2
4

Here's a graphical schedule for this output:
Time     1  2  3  4  5  6  7  8  9 10
Stall 1 c1>>>>>>>>>>>>>>>>>>>>>>>>>>>
Stall 2 .. c2>>>>>> c4>>>>>>>>> .. ..
Stall 3 .. .. c3>>>>>>>>> .. .. .. ..
Stall 4 .. .. .. c5>>>>>>>>> .. .. ..Other outputs using the same number of stalls are possible.