Algorithm

A. A.M. Deviation
time limit per test
1 second
memory limit per test
256 megabytes
Problem link- https://codeforces.com/problemset/problem/1605/A
input
standard input
output
standard output

A number a2�2 is said to be the arithmetic mean of two numbers a1�1 and a3�3, if the following condition holds: a1+a3=2⋅a2�1+�3=2⋅�2.

We define an arithmetic mean deviation of three numbers a1�1, a2�2 and a3�3 as follows: d(a1,a2,a3)=|a1+a3−2⋅a2|�(�1,�2,�3)=|�1+�3−2⋅�2|.

Arithmetic means a lot to Jeevan. He has three numbers a1�1, a2�2 and a3�3 and he wants to minimize the arithmetic mean deviation d(a1,a2,a3)�(�1,�2,�3). To do so, he can perform the following operation any number of times (possibly zero):

  • Choose i,j�,� from {1,2,3}{1,2,3} such that i≠j�≠� and increment ai�� by 11 and decrement aj�� by 11

Help Jeevan find out the minimum value of d(a1,a2,a3)�(�1,�2,�3) that can be obtained after applying the operation any number of times.

Input

The first line contains a single integer t� (1≤t≤5000)(1≤�≤5000)  — the number of test cases.

The first and only line of each test case contains three integers a1�1, a2�2 and a3�3 (1≤a1,a2,a3≤108)(1≤�1,�2,�3≤108).

Output

For each test case, output the minimum value of d(a1,a2,a3)�(�1,�2,�3) that can be obtained after applying the operation any number of times.

Example
input
Copy
3
3 4 5
2 2 6
1 6 5
output
Copy
0
1
0
Note

Note that after applying a few operations, the values of a1�1, a2�2 and a3�3 may become negative.

In the first test case, 44 is already the Arithmetic Mean of 33 and 55.

d(3,4,5)=|3+5−2⋅4|=0�(3,4,5)=|3+5−2⋅4|=0

In the second test case, we can apply the following operation:

(2,2,6)(2,2,6) −→−−−−−−increment a2decrement a1→increment �2decrement �1 (1,3,6)(1,3,6)

d(1,3,6)=|1+6−2⋅3|=1�(1,3,6)=|1+6−2⋅3|=1

It can be proven that answer can not be improved any further.

In the third test case, we can apply the following operations:

(1,6,5)(1,6,5) −→−−−−−−increment a3decrement a2→increment �3decrement �2 (1,5,6)(1,5,6) −→−−−−−−increment a1decrement a2→increment �1decrement �2 (2,4,6)(2,4,6)

d(2,4,6)=|2+6−2⋅4|=0�(2,4,6)=|2+6−2⋅4|=0

 



 

Code Examples

#1 Code Example with C++ Programming

Code - C++ Programming

#include<bits/stdc++.h>
using namespace std;


#define ll long long
#define endl '\n'
#define debug(n) cout<<(n)<<endl;
const ll INF = 2e18 + 99;

int main(){
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);

  int t;
  cin>>t;
  while(t--){
    int a, b, c;
    cin>>a>>b>>c;
    int diff = 2 * b - (a + c);
    (diff % 3 == 0) ? cout<<0<<endl : cout<<1<<endl;
  }

}
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Input

x
–
+
cmd
3
3 4 5
2 2 6
1 6 5

Output

x
–
+
cmd
0
1
0
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Demonstration

Coodeforcess Solution 1605-A A. A.M. Deviation ,C++, Java, Js and Python ,1605-A,Coodeforcess Solution

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