When taking digital photos, it is important to get the proper **exposure** (brightness). A photo can be represented as a grid of by pixels, and the pixel in row and column has a brightness , which can be any real number from to inclusive. If you average the brightnesses of all the pixels in a typical image, the result is . Images whose average is lower than that are **underexposed**, and those whose average is higher are **overexposed**.

Most digital cameras have an exposure correction feature. By choosing a correction constant and multiplying all the pixel brightnesses in an image by , a darker or brighter image can be obtained. **When applying a correction constant, if any pixel brightnesses become greater than 1, those values are "clipped" and reduced to 1.**

Given an image, first determine if it is underexposed, overexposed, or correctly exposed. If the image is not correctly exposed, please find the that would correct its average brightness to . You may consider the image correctly exposed if the required is within of .

#### Constraints

It is guaranteed that no underexposed or overexposed image has a required within of .

#### Input Specification

The first line will contain two space-separated integers, and .

The next lines will each contain space-separated real numbers, the pixel brightnesses.

#### Output Specification

On one line, output the string `underexposed`

, `overexposed`

, or `correctly exposed`

. If the image is not correctly exposed, output an additional line containing one positive real number, the required . Your answer will be considered correct if it has an absolute error of no more than .

#### Sample Input 1

```
2 3
0.36 0.304 0.12
0.408 0.312 0.96
```

#### Sample Output 1

```
underexposed
1.25
```

#### Sample Input 2

```
2 3
0.48 0.58 0.56
0.38 0.40 0.48
```

#### Sample Output 2

`correctly exposed`

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