A checkerboard of $10$ rows and $13$ columns has a number written in each square, beginning in the upper left corner, so that the first row is numbered $1,2,\dots ,13$, the second row $14,15,\dots ,26$, and so on down the board. If the board is renumbered so that the left column, top to bottom, is $1,2,\dots ,10$, the second column $11,12,\dots ,20$ and so on across the board, some squares have the same numbers in both numbering systems. Find the sum of the numbers in these squares (under either system).