2022/055) 2020 distict numbers are in a circle. Show that we can always choose 4 consecutive numbers such that sum of outer 2 numbers is greater than tsom of 2 inner numbers

The 2020 numbers are in a circle. Let the numbers be $a_1$ to $a_{2020}$ now startting wth $a_k$ we have 4 number consecutive $a_k,a_{k+1} ,  a_{k+2}$, $a_{k+3}$ for k from 1 to 2017 and other  4 consecutive  number $a_{2018},a_{2019}, a_{2020}.a_1$ so on

now let us compute the value sum of outer numbers - sum of innter numbers calling $S_n$

$S_{1} = a_{1} - a_{2} - a_{3} + a_{4}$

$S_{2} = a_{2} - a_{3} - a_{4} + a_{5}$

...

...

$S_{2020} = a_{2000} - a_{1} - a{2} + a_3$

If we add all of these then we have

$\sum_{n=1}^{2020}S_{n} = 0$

For the sum of 2020 numbers be zero either all are zero (that means some numbers are same which is not true ) or at least one number is positive say $S_{k}$ then $a_{k}$ is the starting point