# Building the Perfect Array

You are helping a friend who is a computer scientist with a research project. The project requires finding an array that satisfies a certain set of constraints. Specifically, you are given `p` pairs of indices `i` and `j`, where `i` and `j` are indices of an array `a` of length `n`. Each pair `(i, j)` denotes a constraint that must be less than . Your task is to find an array `a` that satisfies all the given constraints.
The integers in the array a should be between 1 and inclusive.

### Input

The first line of the input contains two integers `n` (2 ≤ n ≤ ) and `p` (1 ≤ p ≤ ), where `n` is the length of array a and `p` is the number of pairs. Each of the following `p` lines contains two space-separated integers `i` and `j` (1 ≤ i < j ≤ n), representing the pairs of indices that need to satisfy the constraint .

### Output

If an array a can be found that satisfies all the given constraints, output a single line containing `n` space-separated integers, representing the array `a`. The integers in the array `a` should be between 1 and inclusive. If there are multiple possible solutions, output any one of them.
If it’s not possible to find such an array, the program should print `Impossible`.

#### Examples

 Input Output 4 2 1 2 4 1 2 3 4 1 5 5 1 2 2 3 3 4 5 4 2 5 2 4 6 8 5 3 3 1 2 2 3 3 1 Impossible

#### Constraints

Time limit: 2 seconds

Memory limit: 512 MB

Output limit: 1 MB