Minimax

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Let's consider a square grid with N rows and N columns, both numbered 1 through N. Each cell contains one integer. Let r_{i} denote the minimum value in the ith row, and let C_{i} denote the maximum value in the ith column. A grid is called nice if and only if the following condition holds true:
max(r_{1}, r_{2}, ..., r_{N}) = min(C_{1}, C_{2}, ..., C_{N})
Chef has a square grid and can change some of its elements (numbers in the cells). Find the minimum possible number of elements Chef should change, so that the new grid is nice.
An element can be changed to any integer.
Input
The first line of the input contains an integer N, denoting the size of the grid.
The following N lines describe the grid. The ith of those lines contains N integers, denoting the numbers in the ith row.
Output
Print one integer, denoting the minimum number of changes required to make the grid nice.
Constraints
 1 ≤ N ≤ 1000
 Each number in the initial grid is between 1 and 10^{6}, inclusive.
Examples
Input1: 3 10 20 30 20 10 30 10 5 35 Output1: 1 Input2: 3 10 20 10 20 10 5 30 30 35 Output2: 0 Input3: 4 1 1 3 4 5 1 1 8 9 10 1 1 1 14 15 1 Output3: 2
Explanation
Example #1. In the first example, initially we have r_{1} = 10, r_{2} = 10 and r_{3} = 5. For columns, we have C_{1} = 20, C_{2} = 20 and C_{3} = 35.
max(r_{1}, r_{2}, r_{3}) = 10 and min(C_{1}, C_{2}, C_{3}) = 20, and so the given grid isn't nice. Chef can change the second number in the first row from 20 to 10, to get the following nice grid:
10 10 30 20 10 30 10 5 35
The answer is 1 because we must change at least 1 number.
Example #2. The provided grid is already nice, so the answer is 0.
Author:  errichto 
Tags  errichto 
Date Added:  19062017 
Time Limit:  2 sec 
Source Limit:  50000 Bytes 
Languages:  C, CPP14, JAVA, PYTH, PYTH 3.6, PYPY, CS2, PAS fpc, PAS gpc, RUBY, PHP, GO, NODEJS, HASK, SCALA, D, PERL, FORT, WSPC, ADA, CAML, ICK, BF, ASM, CLPS, PRLG, ICON, SCM qobi, PIKE, ST, NICE, LUA, BASH, NEM, LISP sbcl, LISP clisp, SCM guile, JS, ERL, TCL, PERL6, TEXT, SCM chicken, PYP3, CLOJ, FS 
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