## FONTSIZE - Font Size

### Description

John bought a billboard. He knows what text he wants to put on it, and he has chosen a monospace font to use, but he doesn't know what the font size should be.

Naturally, John wants to use the largest font size possible.

Sizing works as follows:

- The height of a line is the font size.
- The width of a character is two-thirds of the font size.
- Lines can only break between the space-separated words.
- If a space ever falls at the beginning or end of a line, it is omitted.

For example, consider the message "The lazy brown dog".

On a billboard 60 inches wide and 25 inches tall, the maximum font size is 10 inches:

The lazy brown dog

On a billboard 50 inches wide and 50 inches tall, the maximum size is 12.5 inches:

The lazy brown dog

Given the size of the billboard and the message, find the largest font size that will allow the entire message to fix.

### Input

The first line is the width of the billboard in inches, 0 <= W <= 7500, and the height of the billboard in inches, 0 <= H <= 7500.

The third line is the non-empty message, which is comprised of alphanumeric words separated by single spaces. The message is most 10,000 characters long.

The third line is the non-empty message, which is comprised of alphanumeric words separated by single spaces. The message is most 10,000 characters long.

### Output

Print the maximum possible font size, in inches. Your answer must be accurate to within 0.001 of the actual value.

Input | Input |
---|---|

60 25 The lazy brown dog |
50 50 The lazy brown dog |

Output | Output |

10 |
12.5 |

Added by: | BYU Admin |

Date: | 2014-02-23 |

Time limit: | 0.5s |

Source limit: | 50000B |

Memory limit: | 1536MB |

Cluster: | Cube (Intel G860) |

Languages: | All except: ASM64 |