SAT1000 - P936

The torch relay of the Guangzhou 2010 Asian Games was held in cities $A$ , $B$ , $C$ , $D$ , and $E$ . The distance between two of the cities are shown in the table above.

If $A$ was the starting point and $E$ was the ending point, and every city was passed through only once, what would be the minimum total distance travelled of the torch relay?

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