
Fax McClad, Croneria's most defensive bounty hunter, is under attack by the Dankey Kang Gang! He must activate certain defense modes on his personal ship, the Kyuwing, in order to prevent as much damage as possible.
Fax's Kyuwing has
There are
Since repairs can be quite expensive, Fax wants to optimally choose defense modes to activate in order to reduce the amount of damage he receives. Can you tell him the maximum amount of health points that his ship can have after these enemy encounters?
Input Specification
The first line contains three space-separated integers:
Output Specification
The maximum amount of health points that Fax's ship can have remaining, rounded to two decimal places.
If Fax's ship cannot sustain all of the damage, that is, his Kyuwing's health points become DO A BARREL ROLL!
.
Sample Input 1
100 2 2
50 0
0 10
0 10 11
5 1 50
Sample Output 1
60.50
Explanation 1
Fax should utilize defense mode 1 during the fifth second.
During all other times, Fax should switch to defense mode 2 in order to block more of the incoming damage.
Sample Input 2
10 1 1
50 10
3 1 50
Sample Output 2
DO A BARREL ROLL!
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