UCBINTA - Sum

 

Once upon a time, there existed a sequence A consisting of N positive integers. You don't know the

sequence itself, but you do know the sum of every two elements of the sequence. Find the sequence A!

Input

The first line of input contains the positive integer N (2 ≤ N ≤ 1000). Each of the following N lines

contains N positive integers smaller than or equal to 100000, forming the table S. The following relations

hold: S(i, j) = A[i] + A[j] for i ≠ j, and S(i, j) = 0 for i = j. Here S(i, j) denotes the number in the

ith row and jth column of the table, and A[i] denotes the ith element of the sequence A. It is guaranteed

that for any input data set there exists a unique sequence of positive integers A with the given properties.

Output

The first and only line of output must contain the required sequence A (in the form of N space separated

positive integers).

Example

Input:
2
0 2
2 0

Output:
1 1
Input:
4
0 3 6 7
3 0 5 6
6 5 0 9
7 6 9 0

Output:
2 1 4 5

Added by:Gabriel Menacho
Date:2014-09-09
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64
Resource:COCI 2012/2013, round 6, http://www.soj.me/9562

hide comments
2014-11-03 05:51:36 « sudipto »
if n==2, s[0][1]=s[1][0]=always even... :)
2014-10-25 11:17:29 IRFAN
simple maths.. !!!AC in Ist go!!!!
2014-10-02 23:26:07 NOVICE
Not too bad :P
2014-09-25 00:00:07 akshaych
easy one..!! :)
2014-09-24 10:10:53 Rahul Jain
At first, I thought its tough , but WTH, it is very easy
AC in 1st go :)
Score gone +0.45 up :-)

Last edit: 2014-09-27 16:19:53
2014-09-22 22:31:06 :)
easy one .... ac n first go !!
2014-09-21 19:03:47 Vignesh Manoharan
move to tutorial
2014-09-12 15:17:11 Akhilesh Anandh
@Ayush: The problem statement says "It is guaranteed that for any input data set there exists a unique sequence of positive integers A with the given properties." So I guess this won't be given as input.
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