# Increasing triplets

Given 3 arrays

`a`

, `b`

, and `c`

of length `n`

, you are asked to find the number of triplets `(i, j, k)`

such that

. Input

The first line of the input contains a single integer

`n`

(1 ≤ n ≤ ).The next line contains

`n`

integers (0 ≤ ≤ ).The second line contains

`n`

integers (0 ≤ ≤ ).Finally, the third line contains

`n`

integers (0 ≤ ≤ ). Output

The program should print the number of increasing triplets.

Examples

Input | Output |

4
13 6 8 3
1 3 5 8
9 15 7 5 | 7 |

Explanation

#### Constraints

Time limit: 2 seconds

Memory limit: 512 MB

Output limit: 1 MB