1, 2, 3 - Decomposition

AtCoder

IDarc123_c

Time2000ms

Memory256MB

Difficulty—

Given is a positive integer $N$. Consider a sequence of integers $A = (A_1, \ldots, A_K)$ that satisfies the conditions below: * $\sum_{i=1}^K A_i = N$; * each $A_i$ is a positive integer such that every digit in its decimal notation is $1$, $2$, or $3$. Find the minimum possible value of $K$, that is, the number of elements in such a sequence $A$. Process $T$ test cases per input file. ## Constraints * $1\leq T\leq 1000$ * $1\leq N\leq 10^{18}$ ## Input Input is given from Standard Input in the following format: $T$ $\text{case}_1$ $\text{case}_2$ $\vdots$ $\text{case}_T$ Each case is in the following format: $N$ [samples]

Samples

Input #1

Output #1

2
4
1
2
4

For each $N$, one optimal $A$ is shown below.

*   For $N = 456$: $A = (133, 323)$.
*   For $N = 10000$: $A = (323, 3132, 3232, 3313)$.
*   For $N = 123$: $A = (123)$.
*   For $N = 314$: $A = (312,2)$.
*   For $N = 91$: $A = (22,23,23,23)$.

API Response (JSON)

{
  "problem": {
    "name": "1, 2, 3 - Decomposition",
    "description": {
      "content": "Given is a positive integer $N$. Consider a sequence of integers $A = (A_1, \\ldots, A_K)$ that satisfies the conditions below: *   $\\sum_{i=1}^K A_i = N$; *   each $A_i$ is a positive integer such th",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc123_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Given is a positive integer $N$. Consider a sequence of integers $A = (A_1, \\ldots, A_K)$ that satisfies the conditions below:\n\n*   $\\sum_{i=1}^K A_i = N$;\n*   each $A_i$ is a positive integer such th...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments