The integers 1,2,4,5,6,9,10,11,13 are to be placed in the circles and squares below with one number in each shape.
\Large\boxed{x} \bigcirc \square \bigcirc \square \bigcirc \square \bigcirc \boxed{y}
Each integer must be used exactly once and the integer in each circle must be equal to the sum of the integers in the two neighbouring squares. If the integer x is placed in the leftmost square and the integer y is placed in the rightmost square, what is the largest possible value of x+y ?