Without Carry

AtCoder

IDarc136_d

Time4000ms

Memory256MB

Difficulty—

You are given an integer sequence of length $N$: $A=(A_1,A_2,\cdots,A_N)$. Find the number of pairs of integers $(i,j)$ ($1 \leq i < j \leq N$) such that calculation of $A_i+A_j$ by column addition does not involve carrying. ## Constraints * $2 \leq N \leq 10^6$ * $0 \leq A_i \leq 10^6-1$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $A_1$ $A_2$ $\cdots$ $A_N$ [samples]

Samples

Input #1

4
4 8 12 90

Output #1

3

The pairs $(i,j)$ that count are $(1,3),(1,4),(2,4)$.
For example, calculation of $A_1+A_3=4+12$ does not involve carrying, so $(i,j)=(1,3)$ counts. On the other hand, calculation of $A_3+A_4=12+90$ involves carrying, so $(i,j)=(3,4)$ does not count.

Input #2

20
313923 246114 271842 371982 284858 10674 532090 593483 185123 364245 665161 241644 604914 645577 410849 387586 732231 952593 249651 36908

Output #2

Input #3

5
1 1 1 1 1

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Without Carry",
    "description": {
      "content": "You are given an integer sequence of length $N$: $A=(A_1,A_2,\\cdots,A_N)$. Find the number of pairs of integers $(i,j)$ ($1 \\leq i < j \\leq N$) such that calculation of $A_i+A_j$ by column addition do",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 4000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc136_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given an integer sequence of length $N$: $A=(A_1,A_2,\\cdots,A_N)$.\nFind the number of pairs of integers $(i,j)$ ($1 \\leq i < j \\leq N$) such that calculation of $A_i+A_j$ by column addition do...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments