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ACM ICPC 2018 World Finals
Language:
Brookebond s'en va en guerre...
 Time Limit: 1000MS Memory Limit: 65536K Total Submissions: 1764 Accepted: 834 Special Judge

Description

Famous military leader marshal Brookebond who has never lost a battle (truth to be told, he has never won one either) is sincerely convinced that all military operations can be planned on the globe. Let’s not reveal the depth of his misconceptions to the poor marshal. Instead, let’s help him by writing a program to compute the distance between two points on the surface of the Earth given in the geographic coordinates. An order from the marshal Brookebond declares the Earth to be a perfect sphere having radius of 6370 kilometers. And the orders, as we all know, are not to be discussed…

Geographic latitude and longitude are measured in degrees and minutes with the accuracy to one minute (one degree containing 60 minutes, of course). The latitude is measured from 90 degrees of northern latitude (N) for the North Pole to 90 degrees of southern latitude (S) for the South Pole; the latitude of any point on the equator is 0 degrees (N or S, does not matter). The longitude of is measured from 180 degrees of eastern longitude (E) to 180 degrees of western longitude (W); for point on meridians with longitude 180 or 0, E and W are equivalent.

Input

The first and second lines of the input contain the coordinates (latitude and longitude) of one point each. The designation of a latitude contains two integers (degrees and minutes) and a letter N or S. Similarly, the designation of a longitude contains two integers (degrees and minutes) and a letter E or W. Adjacent values on a line are separated by one or more spaces.

Output

The first and only line of the output must contain the distance (in kilometers) between the points from the input file with the precision of 1 meter.

Sample Input

```55 0 N 40 0 E
59 0 N 49 30 E```

Sample Output

`725.979`

Source

Northeastern Europe 2002, Western Subregion

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