123 Triangle

AtCoder

IDagc043_b

Time2000ms

Memory256MB

Difficulty—

Given is a sequence of $N$ digits $a_1a_2\ldots a_N$, where each element is $1$, $2$, or $3$. Let $x_{i,j}$ defined as follows: * $x_{1,j} := a_j$ $\quad$ ($1 \leq j \leq N$) * $x_{i,j} := | x_{i-1,j} - x_{i-1,j+1} |$ $\quad$ ($2 \leq i \leq N$ and $1 \leq j \leq N+1-i$) Find $x_{N,1}$. ## Constraints * $2 \leq N \leq 10^6$ * $a_i = 1,2,3$ $(1 \leq i \leq N)$ ## Input Input is given from Standard Input in the following format: $N$ $a_1$$a_2$$\ldots$$a_N$ [samples]

Samples

Input #1

4
1231

Output #1

1

$x_{1,1},x_{1,2},x_{1,3},x_{1,4}$ are respectively $1,2,3,1$.
$x_{2,1},x_{2,2},x_{2,3}$ are respectively $|1-2| = 1,|2-3| = 1,|3-1| = 2$.
$x_{3,1},x_{3,2}$ are respectively $|1-1| = 0,|1-2| = 1$.
Finally, $x_{4,1} = |0-1| = 1$, so the answer is $1$.

Input #2

10
2311312312

Output #2

API Response (JSON)

{
  "problem": {
    "name": "123 Triangle",
    "description": {
      "content": "Given is a sequence of $N$ digits $a_1a_2\\ldots a_N$, where each element is $1$, $2$, or $3$. Let $x_{i,j}$ defined as follows: *   $x_{1,j} := a_j$ $\\quad$ ($1 \\leq j \\leq N$) *   $x_{i,j} := | x_{i",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc043_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Given is a sequence of $N$ digits $a_1a_2\\ldots a_N$, where each element is $1$, $2$, or $3$. Let $x_{i,j}$ defined as follows:\n\n*   $x_{1,j} := a_j$ $\\quad$ ($1 \\leq j \\leq N$)\n*   $x_{i,j} := | x_{i...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments