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There is an infinite beehive like the one given in the figure. We consider two cells to be adjacent if and only if they share a side. A path of length k from cell c0 to cell ck is a sequence of cells c0, c1, . . . , ck such that ci and ci+1 are adjacent for all 0 ≤ i < k. The distance between cells i and j is the length of the shortest path from cell i to cell j.
The cells of the beehive are indexed using positive integers as shown. The cells with larger distance from cell 1 are given larger indices. The indices of cells with the same distance from cell 1 increases from left to right. Each positive integer is the index of exactly one cell.
We want to know the distance of two cells whose indices are given.
There are multiple test cases in the input. Each test case is a single line containing two space-separated integers i and j as the indices of two cells (1 ≤ i, j ≤ 104). The input terminates with a line containing 0 0 which should not be processed as a test case.
For each test case, output a single line containing the distacne of the given cells.
8 4 11 12 365 365 0 0
2 5 0