Swapping Monkeys

Five monkeys in a circus are sitting in the following order:

The ringmaster wants to reverse their order, but only by swapping the positions of two monkeys at a time.

This is one way, where two swaps take place:

1
2
Swap A and E: E B C D A
Swap B and D: E D C B A

Another possible way takes exactly four swaps:

1
2
3
4
Swap A and E: E B C D A
Swap C and D: E B D C A
Swap B and D: E D B C A
Swap B and C: E D C B A

Is it possible to do this in exactly three swaps?

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