On a checkered paper, numbers $x$, $y$ and $z$ are placed in 3 squares (one number in each), other squares are empty. It is permitted to perform operations of two types:

1) To choose 2 numbers $a$ and $b$ from 2 non-empty squares and to place the number $a + b$ in some empty square;

2) To choose 3 numbers $a$, $b$, and $c$ from 3 non-empty squares and to place the number $ab + c^2$ in some empty square.

Prove that using these operations one can place a number $(x + y + z)^2$ in some square.