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PROBLEM 6 CHAKRAVYUH MARKS 200

Suppose the Great Mahabharatahappens in Kalyug.And suppose you are

Arjuns son Abhimanyu.You are trapped in the middle of a Chakravyuhwith your short range tank (Fig.). The outer circumference represents the

range of the tank. You are surrounded by enemy Maharathishaving their

own tanks. All the enemies tanks are outside inner circle. You cannot harm

the tanks i.e. only shells can be destroyed. You can defend yourself against

their attack by successfully targeting their shells before they reach the inner

circumference. Once they reach the inner circumference, your tank will be

destroyed. The range of the enemies tanks is large enough to reach you.

FIG

But the enemies tanks have a limited number of shells (

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time and fire shells with a fixed interval of time between them. For e.g.

suppose tank 1 start shelling at time t=4 sec and required time for reloading

is 5 seconds then it continue its firing at t=4, 9, 14, 19 until all its shells

are fired. Each tank may have a different starting time and a different

reloading time. Your tanks starting time is t=0 and reloading time 1 sec.

No enemy tank has reloading time less then your tank. Once reloaded

no enemy tank will wait for a moment and fire immediately. However,

your tank may skip some firing ticks, if it is the optimal thing to do for

its savior. e.g.: 103: i.e. at t=0 target=1, at t=1, target=nothing, t=2

target=2.

Your task is to save the tank as long as you can.

NOTE: All shells are assumed to follow straight-line motion.

Input:

There will be a number of test cases. For each Test Case, first line contains a

number n (

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their information is given in the input file.For e.g. the first tank given in

input file is represented as 1, second as 2 and so on.

If you can save yourself up to the time all enemies shells are used, you have

saved your self forever. In that case you just write 1(infinite) as the time up

to which you can save yourself and then give the sequence in which you

target different tanks shells.

While writing the sequence in which you target shells, as you have to

fire continuously at regular interval, there may be some fires that would

not hit any shell inside the firing range. Use 0 as the tank number for

that case, e.g.

At t=0, you hit shell of tank 1.

At t=1, you hit shell of tank 2.

At t=3, you hit shell of tank 1. etc.

Then as you try to fire at t=2, the shell cannot hit anyone because theremay not be any shell inside the range, hence sequence is 1201

Sample Input:

3

400 300 150 0 2 3

-400 200 175 0 2 1

100 300 120 0 2 2

200

100 200

0

Sample Output:

Case 1:

-1

2313101

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