C. Mr. Perfectly Fine
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Victor wants to become "Mr. Perfectly Fine". For that, he needs to acquire a certain set of skills. More precisely, he has $2$ skills he needs to acquire.

Victor has $n$ books. Reading book $i$ takes him $m_i$ minutes and will give him some (possibly none) of the required two skills, represented by a binary string of length $2$.

What is the minimum amount of time required so that Victor acquires all of the two skills?

Input

The input consists of multiple test cases. The first line contains an integer $t$ ($1 \leq t \leq 1000$) — the number of test cases. The description of the test cases follows.

The first line of each test case contains an integer $n$ ($1 \leq n \leq 2 \cdot 10^5$) — the number of books available.

Then $n$ lines follow. Line $i$ contains a positive integer $m_i$ ($1 \leq m_i \leq 2 \cdot 10^5$) and a binary string of length $2$, where $s_{i1} = 1$ if reading book $i$ acquires Victor skill $1$, and $s_{i1} = 0$ otherwise, and $s_{i2} = 1$ if reading book $i$ acquires Victor skill $2$, and $s_{i2} = 0$ otherwise.

It is guaranteed that the sum of $n$ over all test cases doesn't exceed $2 \cdot 10^5$.

Output

For each test case, output a single integer denoting the minimum amount of minutes required for Victor to obtain both needed skills and $-1$ in case it's impossible to obtain the two skills after reading any amount of books.

Example
Input
642 003 104 014 0053 013 015 012 109 1015 1139 118 017 1064 016 017 018 009 011 0048 009 109 118 11
Output
7
5
5
9
-1
8

Note

In the first test case, we can use books $2$ and $3$, with a total amount of minutes spent equal to $3 + 4 = 7$.

In the second test case, we can use the books $1$ and $4$, with a total amount of minutes spent equal to $3 + 2 = 5$.

In the third test case, we have only one option and that is reading book $1$ for a total amount of minutes spent equal to $5$.