There are $25$ towns in a country. Find the smallest $k$ for which one can set up two-direction flight routes connecting these towns so that the following conditions are satisfied:
1) From each town, there are exactly $k$ direct routes to $k$ other towns.
2) If two towns are not connected by a direct route, then there is a town which has direct routes to these two towns.

Let's think step by step and output the final answer within \boxed{}.
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