Takahashi's Information

AtCoder

IDabc088_c

Time2000ms

Memory256MB

Difficulty—

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: $c_{1,1}$ $c_{1,2}$ $c_{1,3}$ $c_{2,1}$ $c_{2,2}$ $c_{2,3}$ $c_{3,1}$ $c_{3,2}$ $c_{3,3}$ [samples]

Samples

Input #1

1 0 1
2 1 2
1 0 1

Output #1

Yes

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

Input #2

2 2 2
2 1 2
2 2 2

Output #2

No

Takahashi is incorrect in this case.

Input #3

0 8 8
0 8 8
0 8 8

Output #3

Yes

Input #4

1 8 6
2 9 7
0 7 7

Output #4

No

API Response (JSON)

{
  "problem": {
    "name": "Takahashi's Information",
    "description": {
      "content": "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 ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc088_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "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.  \nAccording ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments