Add a contradiction to the given sentence.
The birds flew south for the winter.
The birds flew south for the winter, but at the same time, they stayed in the north.
Complete the following task based on the instruction and optional input provided.### Instruction:
Add a contradiction to the given sentence.

### Input:
The birds flew south for the winter.

### Output:
The birds flew south for the winter, but at the same time, they stayed in the north.