## PAINTER - Painter

The local toy store sells small fingerpainting kits with between
three and twelve 50ml bottles of paint, each a different color. The
paints are bright and fun to work with, and have the useful property
that if you mix *X* ml each of any three different colors, you
get *X* ml of gray. (The paints are thick and "airy",
almost like cake frosting, and when you mix them together the volume
doesn't increase, the paint just gets more dense.) None of the
individual colors are gray; the only way to get gray is by mixing
exactly three distinct colors, but it doesn't matter which three. Your
friend Emily is an elementary school teacher and every Friday she does
a fingerpainting project with her class. Given the number of
different colors needed, the amount of each color, and the amount of
gray, your job is to calculate the number of kits needed for
her class.

### Input

The input consists of one or more test cases,
followed by a line containing only zero that signals the end of the
input. Each test case consists of a single line of five or more
integers, which are separated by a space. The first integer *N*
is the number of different colors (3 ≤ *N* ≤ 12). Following
that are *N* different nonnegative integers, each at most 1,000,
that specify the amount of each color needed. Last is a nonnegative
integer *G* ≤ 1,000 that specifies the amount of gray needed.
All quantities are in ml.

### Output

For each test case, output the smallest number of fingerpainting kits sufficient to provide the required amounts of all the colors and gray. Note that all grays are considered equal, so in order to find the minimum number of kits for a test case you may need to make grays using different combinations of three distinct colors.

### Example

Input:3 40 95 21 0 7 25 60 400 250 0 60 0 500 4 90 95 75 95 10 4 90 95 75 95 11 5 0 0 0 0 0 333 0Output:2 8 2 3 4

Added by: | Nikola P Borisov |

Date: | 2008-10-01 |

Time limit: | 0.200s |

Source limit: | 50000B |

Memory limit: | 1536MB |

Cluster: | Cube (Intel G860) |

Languages: | All except: ERL JS-RHINO NODEJS PERL6 VB.NET |

Resource: | ICPC North America Mid-Central Regional Contest 2005 |