+3 +5 +7

AtCoder

IDarc158_a

Time2000ms

Memory256MB

Difficulty—

You are given integers $x_1$, $x_2$, and $x_3$. For these integers, you can perform the following operation any number of times, possibly zero. * Choose a permutation $(i,j,k)$ of $(1,2,3)$, that is, a triple of integers $(i,j,k)$ such that $1\leq i,j,k\leq 3$ and $i\neq j, i\neq k, j\neq k$. * Then, simultaneously replace $x_i$ with $x_i+3$, $x_j$ with $x_j+5$, and $x_k$ with $x_k+7$. Your objective is to satisfy $x_1=x_2=x_3$. Determine whether it is achievable. If it is, print the minimum number of times you need to perform the operation to achieve it. You have $T$ test cases to solve. ## Constraints * $1\leq T\leq 2\times 10^5$ * $1\leq x_1, x_2, x_3 \leq 10^9$ ## Input The input is given from Standard Input in the following format: $T$ $\text{case}_1$ $\vdots$ $\text{case}_T$ Each test case is in the following format: $x_1$ $x_2$ $x_3$ [samples]

Samples

Input #1

4
2 8 8
1 1 1
5 5 10
10 100 1000

Output #1

2
0
-1
315

For the first test case, you can do the following to satisfy $x_1=x_2=x_3$.

*   Perform the operation with $(i,j,k) = (3,2,1)$, replacing $(x_1,x_2,x_3)$ with $(9,13,11)$.
*   Perform the operation with $(i,j,k) = (2,3,1)$, replacing $(x_1,x_2,x_3)$ with $(16,16,16)$.

API Response (JSON)

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      "content": "You are given integers $x_1$, $x_2$, and $x_3$. For these integers, you can perform the following operation any number of times, possibly zero.\n\n*   Choose a permutation $(i,j,k)$ of $(1,2,3)$, that i...",
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