## UCBINTC - Good

You are given a sequence A consisting of N integers (not to be confused with the sequence from a previous

task). We will call the ith sequence element good if it equals the sum of some three elements in positions

strictly smaller than i (an element can be used more than once in the sum). How many good elements

does the sequence contain?

You are given a sequence A consisting of N integers (not to be confused with the sequence from a previous

task). We will call the i^{th} sequence element good if it equals the sum of some three elements in positions

strictly smaller than i (an element can be used more than once in the sum). How many good elements

does the sequence contain?

### Input

The first line of input contains the positive integer N (1 ≤ N ≤ 5000), the length of the se-

quence A. The second line of input contains N space separated integers representing the sequence

A (−100000 ≤ A_{i} ≤ 100000).

### Output

The first and only line of output must contain the number of good elements in the sequence.

### Example

Input:2 1 3Output:1

Input:6 1 2 3 5 7 10Output:4

Input:3 -1 2 0Output:1

Added by: | Gabriel Menacho |

Date: | 2014-09-09 |

Time limit: | 1s |

Source limit: | 50000B |

Memory limit: | 1536MB |

Cluster: | Cube (Intel G860) |

Languages: | All except: ASM64 |

Resource: | 2013年每周一赛第十四场, http://soj.me/9563 |