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Looking for Mathematical Problems of Reasoning from Xiaoshengchu
A, B, C, D and E won the top five in the high jump. After the results were announced, someone asked their ranking:

A said, "B is the third, C is the fifth.

B said: D is the second and E is the fourth.

C said: A first, E fourth.

D said: C first, B second.

E said: D is the second and A is the third.

Half of what they said is true and half is false. Please judge their ranking.