CodePSU 2018 - Intermediate

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2018-03-18 19:00 CET

CodePSU 2018 - Intermediate

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2018-03-18 23:00 CET
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Problem F
Bag Deposit

Tim manages a bag deposit counter. In the morning, people would stop by at his counter to deposit their bags before they go on to do their daily business. They will then come back to collect the bags in the evening each at different times. When people deposit their bags, they will be given a unique id tag for the bag and they need to indicate the time that they will be back to collect their bags. His business has been doing really well but there is one major problem. There are more than $100$ bags each day and Tim can’t just be looking for the bag in the large piles of bags. To optimize his operation he will need to find a way to stack the bags such that he can place them on the stack as they come in and pick the bag from the top of the stack whenever people come back to collect the bags, instead of trying to dig under the pile. And due to limited space, he will need to minimize the number of stacks. There is no limit on how high the stack can be and all the customers will have deposited their bags before anyone comes back to collect their bag.

Input

Input begins with a line containing an integer $n$ representing the number of bags. The next $n$ lines each represents one bag ordered chronologically (so the first bag checked in precedes the second bag checked in, etc.). Each line contains a 4-digit unique bag id followed by the order $r$, ($0 \leq r < 10000$) in which the bag will be collected. For example $2342~ 5$ represents bag with id $2342$ and is the sixth bag that will be collected, where $0$ is the first bag to be collected.

Output

Output the minimal number of stacks needed so that as the bags are collected, they will only be taken from the top of the stack.

Sample Input 1 Sample Output 1
5
0001 4
0002 3
0003 5
0004 1
0005 2
2
Sample Input 2 Sample Output 2
10
0000 1
0001 6
0002 8
0003 2
0004 0
0005 5
0006 3
0007 7
0008 9
0009 4
5