Decreasing then Increasing Permutation

Let $ (a_1,a_2,a_3,\ldots,a_{12}) $ be a permutation of $ (1,2,3,\ldots,12) $ for which <center>$ a_1>a_2>a_3>a_4>a_5>a_6 \mathrm{\ and \ } a_6<a_7<a_8<a_9<a_{10}<a_{11}<a_{12}. $</center> An example of such a permutation is $ (6,5,4,3,2,1,7,8,9,10,11,12). $ Find the number of such permutations.