the number o f partitions

Show that for each positive integer n, the number o f partitions o f n into unequal parts is equal to the number of partitions of n into odd parts.
For example, if n = 6, there are four partitions into unequal parts, namely
                               1 + 5, 1 + 2 + 3, 2+4, 6.
And there are also four partitions into odd parts,
                                                   1 + 1 + 1 + 1 + 1 + 1, 1 + 1 + 1 + 3, 1 +5, 3 + 3.