## MELE2 - ELEVATOR II

English | Vietnamese |

Edward works as an engineer for Non-trivial Elevators: Engineering, Research and Construction (NEERC). His new task is to design a brand new elevator for a skyscraper with h ﬂoors. Edward has an idée fixe: he thinks that four buttons are enough to control the movement of the elevator. His last proposal suggests the following four buttons:

- Move a ﬂoors up.
- Move b ﬂoors up.
- Move c ﬂoors up.
- Return to the ﬁrst ﬂoor.

Initially, the elevator is on the ﬁrst ﬂoor. A passenger uses the ﬁrst three buttons to reach the ﬂoor she needs. If a passenger tries to move a, b or c ﬂoors up and there is no such ﬂoor (she attempts to move higher than the h-th ﬂoor), the elevator doesn’t move. To prove his plan worthy, Edward wants to know how many ﬂoors are actually accessible from the ﬁrst ﬂoor via his elevator. Help him calculate this number.

### Input

The ﬁrst line of the input ﬁle contains one integer h — the height of the skyscraper (1 ≤ h ≤ 10^18). The second line contains three integers a, b and c — the parameters of the buttons (1 ≤ a, b, c ≤ 100000)

### Output

Output one integer number — the number of ﬂoors that are reachable from the ﬁrst ﬂoor.

### Example

Input 1:15 4 7 9Output 1:9

Input 2:500000 160 96 111Output 2:498167

Input 3:987654321987654321 99995 99997 99999Output 3:987654319487854318

Added by: | psetter |

Date: | 2009-02-26 |

Time limit: | 1s |

Source limit: | 50000B |

Memory limit: | 1536MB |

Cluster: | Cube (Intel G860) |

Languages: | All except: C99 ERL JS-RHINO |

Resource: | NEERC 2007–2008 |