There are N kangaroos going out to eat at an Indian restaurant. The ith kangaroo wants to eat *exactly* xi food. The kangaroos all want to order the same size of plates, but each one can order more than one plate for themselves if they need to. If the kangaroo orders more than he needs, he can simply hide the leftovers in his pouch.
At this Indian restaurant, the cost of the plate is the same as its size. Since Karl the Kangaroo is paying and is low on money, he wants to know what is the minimum cost to feed all N kangaroos and what is the largest possible size of the plates that satisfies this minimum cost?
The first line of input is T – the number of test cases.
The first line of each test case is an integer N (1 ≤ N ≤ 105).
The second line contains N space-separated integers xi (1 ≤ xi ≤ 109).
For each test case, output a line containing two space-separated integers – the minimum cost and the maximum plate size that corresponds to when the total cost is minimized.
## Input
The first line of input is T – the number of test cases.The first line of each test case is an integer N (1 ≤ N ≤ 105).The second line contains N space-separated integers xi (1 ≤ xi ≤ 109).
## Output
For each test case, output a line containing two space-separated integers – the minimum cost and the maximum plate size that corresponds to when the total cost is minimized.
[samples]
**Definitions**
Let $ T \in \mathbb{Z} $ be the number of test cases.
For each test case $ k \in \{1, \dots, T\} $:
- Let $ N_k \in \mathbb{Z} $ denote the number of kangaroos, with $ 1 \leq N_k \leq 10^5 $.
- Let $ X_k = (x_{k,1}, x_{k,2}, \dots, x_{k,N_k}) $ be a sequence of positive integers representing the food requirements of each kangaroo, where $ 1 \leq x_{k,i} \leq 10^9 $.
**Constraints**
1. $ 1 \leq T \leq 10^5 $
2. For each test case $ k $:
- $ 1 \leq N_k \leq 10^5 $
- $ 1 \leq x_{k,i} \leq 10^9 $ for all $ i \in \{1, \dots, N_k\} $
**Objective**
For each test case $ k $, find:
- The **minimum total cost** $ C_k $, and
- The **maximum plate size** $ p_k $ such that the total cost is minimized,
where the cost is computed as follows:
For a chosen plate size $ p \in \mathbb{Z}^+ $, each kangaroo $ i $ must order $ \left\lceil \frac{x_{k,i}}{p} \right\rceil $ plates, incurring cost $ p \cdot \left\lceil \frac{x_{k,i}}{p} \right\rceil $.
The total cost is:
$$
C(p) = \sum_{i=1}^{N_k} p \cdot \left\lceil \frac{x_{k,i}}{p} \right\rceil
$$
We seek:
$$
C_k = \min_{p \in \mathbb{Z}^+} C(p), \quad \text{and} \quad p_k = \max \left\{ p \in \mathbb{Z}^+ \mid C(p) = C_k \right\}
$$