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###### Description

Suppose that you want to check if an array of length `n`

contains numbers 1 through `n`

only once, without duplicates.

Write a function `solution`

to return true when the numbers 1 through `n`

only appears once, without duplicates, and false otherwise.

##### Constraints

- Length of array is less than or equal to 100,000.
- Each element of array is an integer between 0 and 100,000.

##### Examples

arr | result |
---|---|

[4, 1, 3, 2] | true |

[4, 1, 3] | false |

Example #1

When [4, 1, 3, 2] is given as input, an array should contain all numbers 1 through 4 because the length of the array is 4. Since [4, 1, 3, 2] contains all numbers 1 through 4, true should be returned.

Example #2

When [4, 1, 3] is given as input, an array should contain all numbers 1 through 3 because the length of the array is 3. However, [4, 1, 3] contains 4 instead of 2, therefore false should be returned.

Result
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