You have three sequences A = a

_{1}, a

_{2},...,a

_{n}, B = b

_{1}, b

_{2},...,b

_{n} and C = c

_{1}, c

_{2},...,c

_{n}. For each 1 <= i <= n it is known that at least one of a

_{i}, b

_{i} and c

_{i} is odd. Prove that there are integers

*r*,

*s* and

*t* such that ra

_{i} + sb

_{i} + tc

_{i} is odd for at least

values of i.