Sqrt

AtCoder

IDabc243_g

Time2000ms

Memory256MB

Difficulty—

We have a sequence of length $1$: $A=(X)$. Let us perform the following operation on this sequence $10^{100}$ times. Operation: Let $Y$ be the element at the end of $A$. Choose an integer between $1$ and $\sqrt{Y}$ (inclusive), and append it to the end of $A$. How many sequences are there that can result from $10^{100}$ operations? You will be given $T$ test cases to solve. It can be proved that the answer is less than $2^{63}$ under the Constraints. ## Constraints * $1 \leq T \leq 20$ * $1 \leq X \leq 9\times 10^{18}$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $T$ $\rm case_1$ $\vdots$ $\rm case_T$ Each case is in the following format: $X$ [samples]

Samples

Input #1

4
16
1
123456789012
1000000000000000000

Output #1

5
1
4555793983
23561347048791096

In the first case, the following five sequences can result from the operations.

*   $(16,4,2,1,1,1,\ldots)$
*   $(16,4,1,1,1,1,\ldots)$
*   $(16,3,1,1,1,1,\ldots)$
*   $(16,2,1,1,1,1,\ldots)$
*   $(16,1,1,1,1,1,\ldots)$

API Response (JSON)

{
  "problem": {
    "name": "Sqrt",
    "description": {
      "content": "We have a sequence of length $1$: $A=(X)$. Let us perform the following operation on this sequence $10^{100}$ times. Operation: Let $Y$ be the element at the end of $A$. Choose an integer between $1$ ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc243_g"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have a sequence of length $1$: $A=(X)$. Let us perform the following operation on this sequence $10^{100}$ times.\nOperation: Let $Y$ be the element at the end of $A$. Choose an integer between $1$ ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments