# Hangover

 Time Limit: 1000MS Memory Limit: 10000K Total Submissions: 85166 Accepted: 40992

Description

How far can you make a stack of cards overhang a table? If you have one card, you can create a maximum overhang of half a card length. (We’re assuming that the cards must be perpendicular to the table.) With two cards you can make the top card overhang the bottom one by half a card length, and the bottom one overhang the table by a third of a card length, for a total maximum overhang of 1/2 + 1/3 = 5/6 card lengths. In general you can make n cards overhang by 1/2 + 1/3 + 1/4 + … + 1/(n + 1) card lengths, where the top card overhangs the second by 1/2, the second overhangs tha third by 1/3, the third overhangs the fourth by 1/4, etc., and the bottom card overhangs the table by 1/(n + 1). This is illustrated in the figure below.

Input

The input consists of one or more test cases, followed by a line containing the number 0.00 that signals the end of the input. Each test case is a single line containing a positive floating-point number c whose value is at least 0.01 and at most 5.20; c will contain exactly three digits.

Output

For each test case, output the minimum number of cards necessary to achieve an overhang of at least c card lengths. Use the exact output format shown in the examples.

Sample Input

```1.00
3.71
0.04
5.19
0.00```

Sample Output

```3 card(s)
61 card(s)
1 card(s)
273 card(s)```

```#include <iostream>
#include <stdio.h>
using namespace std;
int main()
{
int total;
float len[276], tmp;
len[0] = 0;
for (total = 1; len[total-1] <= 5.2; total++) {
tmp = len[total-1] + 1 / (float)(total + 1);
if (tmp <= 5.2) {
len[total] = tmp;
} else {
break;
}
}

float input;
while (cin>>input) {
if (input == 0.00) {
return 0;
}
int left, right, middle;
left = 0;
right = total;
while (left + 1 < right) {
middle = (right + left) / 2;
if (len[middle] < input) {
left = middle;
} else {
right = middle;
}
}
cout<<right<<" card(s)"<<endl;
}
return 0;
}```
 Result Memory Time Language Code Length Accepted 256K 0MS C++ 653B

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