COCI '12 Contest 6 #2 Sume

Points: 7

Time limit: 1.0s

Memory limit: 32M

Problem type

Once upon a time, there existed a sequence $A$ $A$ consisting of $N$ $N$ 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 $A$ $A$ !

Input Specification

The first line of input contains the positive integer $N$ $N$ $(2 \le N \le 1000)$ $(2 \leq N \leq 1000)$ .

Each of the following $N$ $N$ lines contains $N$ $N$ positive integers smaller than or equal to $100\,000$ $100 000$ , forming the table $S$ $S$ . The following relations hold: $S(i, j) = A[i] + A[j]$ $S (i, j) = A [i] + A [j]$ for $i \neq j$ $i \neq j$ , and $S(i, j) = 0$ $S (i, j) = 0$ for $i = j$ $i = j$ . Here $S(i, j)$ $S (i, j)$ denotes the number in the $i^\text{th}$ $i^{th}$ row and $j^\text{th}$ $j^{th}$ column of the table, and $A[i]$ $A [i]$ denotes the $i^\text{th}$ $i^{th}$ element of the sequence $A$ $A$ .

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

Output Specification

The first and only line of output must contain the required sequence $A$ $A$ (in the form of $N$ $N$ space-separated positive integers).

Sample Input 1

Copy

2
0 2
2 0

Sample Output 1

Copy

1 1

Sample Input 2

Copy

Sample Output 2

Copy

2 1 4 5

Comments

0

darek commented on March 31, 2022, 3:48 p.m. ← edited →

Is 0 a positive integer /s?

3

Spitfire720 commented on March 31, 2022, 5:19 p.m.

no/s