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UPCOMING CHALLENGES:

CURRENT CHALLENGES:

Palladium 2020

PAST CHALLENGES

Rhodium 2019

Ruthenium 2019

Technetium 2019

Molybdenum 2019

Niobium 2019

Zirconium 2019

Yttrium 2019

Strontium 2019

Rubidium 2018

Arsenicum 2018

Krypton 2018

Bromum 2018

Future Mobility

Grand Challenge

Digital Gold

Selenium 2018

Germanium 2018

Gallium 2018

Zinc 2018

Cuprum 2018

Cutting Complexity

Nickel 2018

Cobaltum 2018

Ferrum 2018

Manganum 2017

Chromium 2017

Vanadium 2016

Titanium 2016

Scandium 2016

Calcium 2015

Kalium 2015

Argon 2015

Chlorum 2014

Sulphur 2014

Phosphorus 2014

Silicium 2014

Aluminium 2014

Magnesium 2014

Natrium 2014

Neon 2014

Fluorum 2014

Oxygenium 2014

Nitrogenium 2013

Carbo 2013

Boron 2013

Beryllium 2013

Lithium 2013

Helium 2013

Hydrogenium 2013

Omega 2013

Psi 2012

Chi 2012

Phi 2012

Upsilon 2012

Tau 2012

Sigma 2012

Rho 2012

Pi 2012

Omicron 2012

Xi 2012

Nu 2011

Mu 2011

Lambda 2011

Kappa 2011

Iota 2011

Theta 2011

Eta 2011

Zeta 2011

Epsilon 2011

Delta 2011

Gamma 2011

Beta 2010

Alpha 2010

Programming language:

You are given N round clocks.

Every clock has M hands, and these hands can point to positions 1, 2, 3, ..., P (yes, these represent numbers around each face). The clocks are represented by the matrix A consisting of N rows and M columns of integers. The first row represents the hands of the first clock, and so on.

For example, you are given matrix A consisting of five rows and two columns, and P = 4:

You can rotate the clocks to obtain several clocks that look identical. For example, if you rotate the third, fourth and fifth clocks you can obtain the following clocks:

After rotation, the first, third and fourth clocks look the same, and the second clock looks the same as the fifth one. That means there are four pairs of clocks that look the same: (1, 3), (1, 4), (2, 5) and (3, 4).

Write a function:

class Solution { public int solution(int[][] A, int P); }

that, given a zero-indexed matrix A consisting of N rows and M columns of integers and integer P, returns the maximal number of pairs of clocks that can look the same after rotation.

For example, given the following array A and P = 4:

the function should return 4, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N and M are integers within the range [1..500];
- P is an integer within the range [1..1,000,000,000];
- each element of matrix A is an integer within the range [1..P];
- the elements of each row of matrix A are all distinct.

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