Uncle M

SUB Inter University Prog...
Limits 2s, 512 MB

J's uncle Mr. M is obsessed with statistics. Wherever he finds data he likes to apply statistical analysis on that. J being his nephew M expects him to be good on statistical analysis as well. Today he's come to J with a 2D matrix of numbers from GOD knows where. Now he's choosing a rectangular portion from that matrix and asking J to calculate the variance of that portion. J is not that bad at statistics as well but needs your help to double check the answer before telling it to uncle M. Are you up for helping J?

For a set of numbers a1, a2, a3, … … … , an their variance is defined as ―

where

Input

The first the of the input contains r(1≤r≤1000) and c(1≤c≤1000), the number of rows and the numbers of columns in the matrix. Then r lines follows with c numbers each. The number at i-th row and j-th column is aij(1≤aij≤10^5).
Then there is q(1≤q≤10^5) on a single line. Then follows q lines with four numbers x1, y1, x2, y2(1<=x1<=x2<=r, 1<=y1<=y2<=c) each where (x1, y1) is the upper left coordinate of the rectangle and (x2, y2) is the lower right coordinate of the rectangle.

Output

For each query in the input output the variance of that rectangle on a single line. Errors less than 10-4 will be ignored.

Sample

InputOutput
2 2
84 87 
78 16 
2
1 1 1 2
1 1 2 2
2.2500000000
852.1875000000

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Statistics

100% Solution Ratio
Neaj_MorshadEarliest, 2w ago
ShamimSarkerFastest, 0.1s
NaheedLightest, 34 MB
NaheedShortest, 1583B
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