Problem:
Score: 300 points

Problem Statement

We have a 3 \times 3 grid. A number c_{i, j} is written in the square (i, j), where (i, j) denotes the square at the i-th row from the top and the j-th column from the left.

According to Takahashi, there are six integers a_1, a_2, a_3, b_1, b_2, b_3 whose values are fixed, and the number written in the square (i, j) is equal to a_i + b_j.

Determine if he is correct.

Constraints

c_{i, j} \ (1 \leq i \leq 3, 1 \leq j \leq 3) is an integer between 0 and 100 (inclusive).

Input

Input is given from Standard Input in the following format:

c_{1,1} c_{1,2} c_{1,3}
c_{2,1} c_{2,2} c_{2,3}
c_{3,1} c_{3,2} c_{3,3}

Output

If Takahashi's statement is correct, print Yes; otherwise, print No.

Sample Input 1

1 0 1
2 1 2
1 0 1

Sample Output 1

Yes

Takahashi is correct, since there are possible sets of integers such as: a_1=0,a_2=1,a_3=0,b_1=1,b_2=0,b_3=1.

Sample Input 2

2 2 2
2 1 2
2 2 2

Sample Output 2

No

Takahashi is incorrect in this case.

Sample Input 3

0 8 8
0 8 8
0 8 8

Sample Output 3

Yes

Sample Input 4

1 8 6
2 9 7
0 7 7

Sample Output 4

No

Solution in Rust (1.15.1) (judge verdict: Accepted)

#[allow(unused_imports)]
use std::io::{stdin, Read, StdinLock};
#[allow(unused_imports)]
use std::cmp::{max, min, Ordering};
#[allow(unused_imports)]
use std::str::FromStr;
#[allow(unused_imports)]
use std::collections::{HashSet, HashMap, BinaryHeap, VecDeque};
#[allow(unused_imports)]
use std::vec::Vec;

#[allow(dead_code)]
const INF: i32 = 1000_000_000;
#[allow(dead_code)]
const INFLL: i64 = 1000_000_000_000_000_000;
#[allow(dead_code)]
const EPS: f64 = 1.0e-10;
#[allow(dead_code)]
const MOD: i32 = 1000_000_007;
#[allow(dead_code)]
const MODLL: i64 = 1000_000_007;

struct Scanner<'a> {
    cin: StdinLock<'a>,
}

#[allow(dead_code)]
impl<'a> Scanner<'a> {
    fn new(cin: StdinLock<'a>) -> Scanner<'a> {
        Scanner {cin: cin}
    }
    fn read1<T: FromStr>(&mut self) -> Option<T> {
        let token = self.cin.by_ref().bytes().map(|c| c.unwrap() as char)
                    .skip_while(|c| c.is_whitespace())
                    .take_while(|c| !c.is_whitespace())
                    .collect::<String>();
        token.parse::<T>().ok()
    }
    fn read<T: FromStr>(&mut self) -> T {
        self.read1().unwrap()
    }
}



fn main() {
    let cin = stdin();
    let cin = cin.lock();
    let mut sc = Scanner::new(cin);

    let mut c: Vec<Vec<i32>> = vec![vec![0; 3]; 3];
    for i in 0..3 {
        for j in 0..3 {
            c[i][j] = sc.read();
        }
    }
    let mut ans = false;
    for a1 in -100..100i32 {
        for a2 in -100..100i32 {
            for a3 in -100..100i32 {
                let b: Vec<i32> = vec![c[0][0] - a1, c[0][1] - a1, c[0][2] - a1];
                let a: Vec<i32> = vec![a1, a2, a3];
                let mut t = true;
                for i in 0..3 {
                    for j in 0..3 {
                        if a[i] + b[j] != c[i][j] {
                            t = false;
                        }
                    }
                }
                ans |= t;
            }
        }
    }
    if ans {
        println!("Yes");
    } else {
        println!("No");
    }
}