On a chess tournament two teams $A$ and $B$ are playing between each other and each consists of $n$ participants. It was noticed that however they arranged them in pairs, there was at least one pair that already played a match. Prove that there can be chosen $a$ chess players from $A$ and $b$ chess players from $B$ so that $a+b>n$ and each from the first chosen group has played a match earlier with each from the second group.