GUESS THE ARRAY

Chef and Chefina plays a game of guessing an array of integers. Chefina has an array of size $ N $. She forms a $N * N$ matrix by calculating the Greatest Common Divisor of each element with all other elements.(That is $ Matrix[i][j]=GCD(i,j)$). She gives Chef all the elements of the matrix, but in some random order. Chef has to guess the original array. Chef cannot find the solution