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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)


#include <stdio.h>
#include <iostream>
#include <string.h>
#include <limits.h>
#include <string>
#include <vector>
#include <algorithm>
#include <map>

#ifndef ULLONG
typedef unsigned long long ULLONG;
#endif
#ifndef LLONG
typedef long long LLONG;
#endif
template <class _T> static _T tp_abs(const _T& a) {
	return ((a < 0) ? (a * -1) : a);
}
template <class _T> static void tp_swap(_T& right, _T& left) {
	//	usage:  tp_swap<type name>(a, b);
	_T tmp = right;
	right = left;
	left = tmp;
}
template <class _T> static _T tp_min(_T a, _T b) {
	return a < b ? a : b;
}
template <class _T> static _T tp_max(_T a, _T b) {
	return a > b ? a : b;
}
template<class _T> static void get1int(_T& a) {
	const char* fmt = " %d";
	if (sizeof(_T) == sizeof(long long)) {
		fmt = " %lld";
	}

	if (scanf(fmt, &a) < 0) {
		printf("g1int Error\n");
	}
}
template<class _T> static void get2int(_T& a, _T& b) {
	const char* fmt = " %d %d";
	if (sizeof(_T) == sizeof(long long)) {
		fmt = " %lld %lld";
	}

	if (scanf(fmt, &a, &b) < 0) {
		printf("g2int Error\n");
	}
}
template<class _T> static void get3int(_T& a, _T& b, _T& c) {
	const char* fmt = " %d %d %d";
	if (sizeof(_T) == sizeof(long long)) {
		fmt = " %lld %lld %lld";
	}

	if (scanf(fmt, &a, &b, &c) < 0) {
		printf("g3int Error\n");
	}
}
static void getstring(char* buff) {
	if (scanf(" %s", buff) < 0) {
		printf("getstr error!\n");
	}
}

static void ABC088C_TakahashisInfomation();

#if 1
int main()
{
	ABC088C_TakahashisInfomation();
	fflush(stdout);
	return 0;
}
#endif

static void ABC088C_TakahashisInfomation()
{
	int cNum[3][3] = { 0 };
	for (int i = 0; i < 3; i++) {
		for (int j = 0; j < 3; j++) {
			get1int(cNum[i][j]);
		}
	}
	
	int csum1[3] = { 0 };
	for (int i = 0; i < 3; i++) {
		for (int j = 0; j < 3; j++) {
			csum1[i] += cNum[j][i];
		}
	}

	for (int i = 0; i <= 100; i++) {
		for (int j = 0; j <= 100; j++) {
			for (int k = 0; k <= 100; k++) {
				if (((3 * i - 3 * j) == (csum1[0] - csum1[1])) &&
					((3 * i - 3 * k) == (csum1[1] - csum1[2]))) {
					printf("Yes\n");
					return;
				}
			}
		}
	}
	printf("No\n");
}