Greater Than Average

AtCoder

IDarc197_b

Time2000ms

Memory256MB

Difficulty—

Define the **score** of a non-empty integer sequence $x = (x_1, \ldots, x_n)$ as the number of elements of $x$ that are strictly greater than the average of $x$. That is, the score of $x$ is the count of indices $i$ satisfying $x_i > \dfrac{x_1+\cdots+x_n}{n}$. You are given a length-$N$ integer sequence $A = (A_1, \ldots, A_N)$. Find the maximum score of a non-empty subsequence of $A$. There are $T$ test cases; solve each one. Definition of subsequence A subsequence of $A$ is any sequence obtained by deleting zero or more elements from $A$ and keeping the remaining elements in their original order. ## Constraints * $1\le T\le 2\times 10^5$ * $2\le N\le 2\times 10^5$ * $1\le A_i\le 10^9$ * All input values are integers. * The sum of $N$ over all test cases is at most $2\times 10^5$. ## Input The input is given from Standard Input in the following format: $T$ $\text{case}_1$ $\vdots$ $\text{case}_T$ Each case is given in the following format: $N$ $A_1$ $\cdots$ $A_N$ [samples]

Samples

Input #1

3
5
2 6 5 7 5
5
10 10 10 10 10
5
1 10 100 1000 10000

Output #1

3
0
1

For the first test case, below are examples of subsequences, their averages, and their scores.

*   $x = (A_1) = (2)$: the average is $2$, and the score is $0$.
*   $x = (A_3,A_5) = (5,5)$: the average is $5$, and the score is $0$.
*   $x = (A_1,A_3,A_4,A_5) = (2,5,7,5)$: the average is $\frac{19}{4}$, and the score is $3$.
*   $x = (A_1,A_2,A_3,A_4,A_5) = (2,6,5,7,5)$: the average is $5$, and the score is $2$.

API Response (JSON)

{
  "problem": {
    "name": "Greater Than Average",
    "description": {
      "content": "Define the **score** of a non-empty integer sequence $x = (x_1, \\ldots, x_n)$ as the number of elements of $x$ that are strictly greater than the average of $x$. That is, the score of $x$ is the count",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc197_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Define the **score** of a non-empty integer sequence $x = (x_1, \\ldots, x_n)$ as the number of elements of $x$ that are strictly greater than the average of $x$.\nThat is, the score of $x$ is the count...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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