Japanese Sums and Loop (589)

Place a digit from 1 to 6 (1 to 4 in the example) into some cells so that no digit appears more than once in each row or column. Cells may remain empty. Numbers outside the grid indicate the sums of continuous groups of digits (including “sums” of a single digit). These sums are given in the same order as their corresponding groups of digits. It must be possible to draw a loop that passes through all the empty cells that only consists of vertical and horizontal segments between cell centers and does not use any cell more than once.

Reference: WPF (1)