Frog VS mosquito: the last fight!

The forest swamp is divided into 8 \times 8 identical cells. A frog is sitting in one of the cells, and a mosquito is flying above some other cell. The frog wants to eat the mosquito, and the mosquito tries to escape (avoiding death in the frog's belly). The frog and the mosquito move in turn.

In one jump, the frog can move horizontally or vertically by any nonzero number of cells. The mosquito, in a single move, can fly to any of the $8$ neighboring cells (horizontally, vertically, or diagonally). If the frog jumps through a cell where the mosquito is, or lands directly on that cell, the frog eats the mosquito. The frog can also move diagonally by one cell if this move allows it to eat the mosquito.

Write a program that, given the initial positions of the frog and the mosquito, determines whether the frog can eat the mosquito.

The frog and mosquito must move each turn (cannot stay in place). The mosquito and frog may occupy the same cell, but if this happens on the frog's move, then no sequence of moves will allow the frog to eat the mosquito.

\InputFileThe input contains several (up to $1000$) tests. Each test is given on a separate line and contains $5$ numbers: X_L Y_L X_K Y_K $M$, space separated. Here, X_L, Y_L are the frog's initial coordinates, X_K, Y_K are the mosquito's initial coordinates, and $M$ indicates who moves first: $0$ for the frog, $1$ for the mosquito.

The end of the test cases is indicated by a single $0$ on a separate line.

\OutputFilePrint the answer for each test on a separate line. Print YES if, under the optimal strategies of both, the frog will eat the mosquito, and NO otherwise.