1651 - [Usaco2006 Feb]Stall Reservations 专用牛棚

Oh those picky N (1 <= N <= 50,000) cows! They are so picky that each one will only be milked over some precise time interval A..B (1 <= A <= B <= 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 有N头牛,每头牛有个喝水时间,这段时间它将专用一个Stall 现在给出每头牛的喝水时间段,问至少要多少个Stall才能满足它们的要求

Input

  • Line 1: A single integer, N
  • Lines 2..N+1: Line i+1 describes cow i's milking interval with two space-separated integers.

Output

  • 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.

Examples

Input

5
1 10
2 4
3 6
5 8
4 7

Output

4


OUTPUT DETAILS:

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.

Hint

不妨试下这个数据,对于按结束点SORT,再GREEDY的做法 1 3 5 7 6 9 10 11 8 12 4 13 正确的输出应该是3

Time Limit 1 second
Memory Limit 128 MB
Stats
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