Problem 777

In three cells of a grid sheet, numbers are written, while the other cells are empty. It is allowed to choose two numbers from different non-empty cells and write their sum in an empty cell; also, one can choose numbers $a, b, c$ from three different non-empty cells and write the number $a b+c^{2}$ in an empty cell. Prove that using several such operations, one can write the square of the sum of the three initial numbers (regardless of what they are) in one of the cells.