Orthogonality

AtCoder

IDabc188_b

Time2000ms

Memory256MB

Difficulty—

Given are two $N$\-dimensional vectors $A = (A_1, A_2, A_3, \dots, A_N)$ and $B = (B_1, B_2, B_3, \dots, B_N)$. Determine whether the inner product of $A$ and $B$ is $0$. In other words, determine whether $A_1B_1 + A_2B_2 + A_3B_3 + \dots + A_NB_N = 0$. ## Constraints * $1 \le N \le 100000$ * $-100 \le A_i \le 100$ * $-100 \le B_i \le 100$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $A_1$ $A_2$ $A_3$ $\dots$ $A_N$ $B_1$ $B_2$ $B_3$ $\dots$ $B_N$ [samples]

Samples

Input #1

2
-3 6
4 2

Output #1

Yes

The inner product of $A$ and $B$ is $(-3) \times 4 + 6 \times 2 = 0$.

Input #2

2
4 5
-1 -3

Output #2

No

The inner product of $A$ and $B$ is $4 \times (-1) + 5 \times (-3) = -19$.

Input #3

3
1 3 5
3 -6 3

Output #3

Yes

The inner product of $A$ and $B$ is $1 \times 3 + 3 \times (-6) + 5 \times 3 = 0$.

API Response (JSON)

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    "name": "Orthogonality",
    "description": {
      "content": "Given are two $N$\\-dimensional vectors $A = (A_1, A_2, A_3, \\dots, A_N)$ and $B = (B_1, B_2, B_3, \\dots, B_N)$.   Determine whether the inner product of $A$ and $B$ is $0$.   In other words, determine",
      "description_type": "Markdown"
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    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
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    {
      "statement_type": "Markdown",
      "content": "Given are two $N$\\-dimensional vectors $A = (A_1, A_2, A_3, \\dots, A_N)$ and $B = (B_1, B_2, B_3, \\dots, B_N)$.  \nDetermine whether the inner product of $A$ and $B$ is $0$.  \nIn other words, determine...",
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      "language": "English"
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