Given an array of

`n`

integers, you are asked if it’s possible to slice the array into 3 non-empty parts so that those 3 parts have the same sum. Input

The first line of the input contains an integer

`n`

- the number of items in the array (1 ≤ n ≤ ).The next line contains

`n`

integers separated by a space, that represent the array elements . Output

The program should print

`Yes`

if it’s possible to slice the array in 2 places to have 3 non-empty parts of equal sums, and `No`

otherwise. Examples

Input | Output |

5
3 2 1 3 0 | Yes |

4
5 -1 0 6 | No |

Explanation

- [3] [2, 1] [3, 0] ⇒ all parts sum up to 3

- No configuration leads to 3 parts of the same sum