Invariants and Monovariants in Dynamical Systems

There are $20$ geese numbered $1-20$ standing in a line. The even numbered geese are standing at the front in the order $2,4,\dots,20$, where $2$ is at the front of the line. Then the odd numbered geese are standing behind them in the order, $1,3,5,\dots ,19$, where $19$ is at the end of the line. The geese want to rearrange themselves in order, so that they are ordered $1,2,\dots,20$ (1 is at the front), and they do this by successively swapping two adjacent geese. What is the minimum number of swaps required to achieve this formation?

Source: 2011-2012 Winter Online Math Open