IT-CESENATICO 1994 Problem 6

The squares of a $10 \times 10$ chessboard are labelled with $1,2,...,100$ in the usual way: the $i$ -th row contains the numbers $10i -9,10i - 8,...,10i$ in increasing order. The signs of fifty numbers are changed so that each row and each column contains exactly five negative numbers. Show that after this change the sum of all numbers on the chessboard is zero.