that the square in the north-west corner has coordinates (1, 1) and the square in
the south-east corner has coordinates (n, m). See the picture in the notes for
clarifications.
Before the game show the organizers offer Yura to occupy any of the
(n + 1)·(m + 1) intersection points of the dividing lines. After that he can start
guessing the cars. After Yura chooses a point, he will be prohibited to move along
the parking lot before the end of the game show. As Yura is a car expert, he will
always guess all cars he is offered, it's just a matter of time. Yura knows that to
guess each car he needs to spend time equal to the square of the euclidean
distance between his point and the center of the square with this car, multiplied by
some coefficient characterizing the machine's "rarity" (the rarer the car is, the harder
it is to guess it). More formally, guessing a car with "rarity" c placed in a square
whose center is at distance d from Yura takes c·d
2
seconds. The time Yura spends
on turning his head can be neglected.
It just so happened that Yura knows the "rarity" of each car on the parking lot in
advance. Help him choose his point so that the total time of guessing all cars is the
smallest possible.
Input
The first line contains two integers n and m (1 ≤ n, m ≤ 1000) — the sizes of the
parking lot. Each of the next n lines contains m integers: the j-th number in the i-th
line describes the "rarity" c
ij
(0 ≤ c
ij
≤ 100000) of the car that is located in the
square with coordinates (i, j).
Output
In the first line print the minimum total time Yura needs to guess all offered cars. In
the second line print two numbers l
i
and l
j
(0 ≤ l
i
≤ n, 0 ≤ l
j
≤ m) — the numbers of
dividing lines that form a junction that Yura should choose to stand on at the
beginning of the game show. If there are multiple optimal starting points, print the
point with smaller l
i
. If there are still multiple such points, print the point with smaller
l
j
.
Please do not use the %lld specifier to read or write 64-bit integers in С++. It is
preferred to use the cin, cout streams or the %I64d specifier.
Sample test(s)
Input
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