Reflection

AtCoder

IDagc057_f

Time3000ms

Memory256MB

Difficulty—

There are three indistinguishable stones at integer coordinates on a number line. Consider the following operation on these stones: * Let $A, B, C$ be the three stones in ascending order of coordinate (ties broken arbitrarily). Perform one of the following. * Move $A$ to the symmetric position with respect to $B$. * Move $C$ to the symmetric position with respect to $B$. You are given the initial coordinates $a, b, c$ of the three stones. Find the number, modulo $998244353$, of possible combinations of coordinates of the three stones after zero or more operations. Note that the stones are indistinguishable. More strictly speaking, count the possible **multisets** of coordinates of the three stones. We will give you $T$ test cases; solve each of them. ## Constraints * $1\leq T\leq 10^5$ * $-10^{18}\leq a\leq b\leq c\leq 10^{18}$ ## Input Input is given from Standard Input in the following format: $T$ $\text{case}_1$ $\vdots$ $\text{case}_T$ Each case is in the following format: $a$ $b$ $c$ [samples]

Samples

Input #1

6
1 3 5
-2 -2 5
0 1 3
31 41 59
-123456789 0 987654321
-1000000000000000000 0 1000000000000000000

Output #1

5
2
9
70
182333351
5

For $(a,b,c) = (1,3,5)$, the five possible combinations of the three stones after operations are:

*   $(1,3,5)$, $(1,1,3)$, $(-1,1,1)$, $(3,5,5)$, $(5,5,7)$.

The figure below may be helpful.
  

![image](https://img.atcoder.jp/agc057/5fc6a5c57abe2c69d457111ddc3f6a51.png)

API Response (JSON)

{
  "problem": {
    "name": "Reflection",
    "description": {
      "content": "There are three indistinguishable stones at integer coordinates on a number line. Consider the following operation on these stones: *   Let $A, B, C$ be the three stones in ascending order of coordin",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 3000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc057_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are three indistinguishable stones at integer coordinates on a number line. Consider the following operation on these stones:\n\n*   Let $A, B, C$ be the three stones in ascending order of coordin...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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