I. Goofy Numbers

Codeforces

IDCF72I

Time2000ms

Memory256MB

Difficulty—

implementation

English · Original

Chinese · Translation

Formal · Original

The non-negative integer _a_ is a divisor of the non-negative integer _b_ if and only if there exists a **positive** integer _c_ such that _a_ × _c_ = _b_. Some numbers are really interesting. Commander Surena defines some interesting properties for non-negative integers: * An integer is happy if it is divisible by at least one of its digits and not by all of them. * An integer is happier if it is divisible by all of its digits. * An integer is upset if it's divisible by none of its digits. Surena asks you to find out if a given number is happy, happier or upset. ## Input Input contains a single non-negative integer _n_ (1 ≤ _n_ ≤ 108). ## Output Write on a single line the type of the integer: _happy_, _happier_ or _upset_. Print the type in lowercase letters. [samples] ## Note In the second test 29994 is only divisible by 2. In the third test 23 is a prime number.

非负整数 #cf_span[a] 是非负整数 #cf_span[b] 的因数，当且仅当存在一个 *正* 整数 #cf_span[c] 使得 #cf_span[a × c = b]。某些数字非常有趣。指挥官 Surena 为非负整数定义了一些有趣的性质： Surena 要求你判断给定的数字是 happy、happier 还是 upset。输入包含一个非负整数 #cf_span[n]（#cf_span[1 ≤ n ≤ 108]）。请在一行中输出该整数的类型：_happy_、_happier_ 或 _upset_。请用小写字母打印类型。在第二个测试中，#cf_span[29994] 仅能被 #cf_span[2] 整除。在第三个测试中，#cf_span[23] 是一个质数。 ## Input 输入包含一个非负整数 #cf_span[n]（#cf_span[1 ≤ n ≤ 108]）。 ## Output 请在一行中输出该整数的类型：_happy_、_happier_ 或 _upset_。请用小写字母打印类型。 [samples] ## Note 在第二个测试中，#cf_span[29994] 仅能被 #cf_span[2] 整除。在第三个测试中，#cf_span[23] 是一个质数。

**Definitions** Let $ n \in \mathbb{Z}_{\geq 0} $. Let $ D(n) = \{ d \in \mathbb{Z}^+ \mid d \mid n \} $ denote the set of positive divisors of $ n $. Let $ \sigma(n) = |D(n)| $ denote the number of positive divisors of $ n $. **Constraints** $ 1 \leq n \leq 10^8 $ **Objective** Classify $ n $ as: - **happy**, if $ \sigma(n) = 2 $, - **happier**, if $ \sigma(n) = 3 $, - **upset**, otherwise.

Samples

Input #1

Output #1

happier

Input #2

Output #2

happy

Input #3

Output #3

upset

API Response (JSON)

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  "problem": {
    "name": "I. Goofy Numbers",
    "description": {
      "content": "The non-negative integer _a_ is a divisor of the non-negative integer _b_ if and only if there exists a **positive** integer _c_ such that _a_ × _c_ = _b_. Some numbers are really interesting. Comman",
      "description_type": "Markdown"
    },
    "platform": "Codeforces",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "CF72I"
  },
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    {
      "statement_type": "Markdown",
      "content": "The non-negative integer _a_ is a divisor of the non-negative integer _b_ if and only if there exists a **positive** integer _c_ such that _a_ × _c_ = _b_.\n\nSome numbers are really interesting. Comman...",
      "is_translate": false,
      "language": "English"
    },
    {
      "statement_type": "Markdown",
      "content": "非负整数 #cf_span[a] 是非负整数 #cf_span[b] 的因数，当且仅当存在一个 *正* 整数 #cf_span[c] 使得 #cf_span[a × c = b]。\n\n某些数字非常有趣。指挥官 Surena 为非负整数定义了一些有趣的性质：\n\nSurena 要求你判断给定的数字是 happy、happier 还是 upset。\n\n输入包含一个非负整数 #cf_span[n]（#cf...",
      "is_translate": true,
      "language": "Chinese"
    },
    {
      "statement_type": "Markdown",
      "content": "**Definitions**  \nLet $ n \\in \\mathbb{Z}_{\\geq 0} $.  \nLet $ D(n) = \\{ d \\in \\mathbb{Z}^+ \\mid d \\mid n \\} $ denote the set of positive divisors of $ n $.  \nLet $ \\sigma(n) = |D(n)| $ denote the numbe...",
      "is_translate": false,
      "language": "Formal"
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}

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