human
You are given n integers a_1, a_2, …, a_n. Find the maximum value of max(a_l, a_{l + 1}, …, a_r) ⋅ min(a_l, a_{l + 1}, …, a_r) over all pairs (l, r) of integers for which 1 ≤ l < r ≤ n.

Input

The first line contains a single integer t (1 ≤ t ≤ 10 000) — the number of test cases.

The first line of each test case contains a single integer n (2 ≤ n ≤ 10^5).

The second line of each test case contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^6).

It is guaranteed that the sum of n over all test cases doesn't exceed 3 ⋅ 10^5.

Output

For each test case, print a single integer — the maximum possible value of the product from the statement.

Example

Input

4
3
2 4 3
4
3 2 3 1
2
69 69
6
719313 273225 402638 473783 804745 323328

Output

12
6
4761
381274500335

Note

Let f(l, r) = max(a_l, a_{l + 1}, …, a_r) ⋅ min(a_l, a_{l + 1}, …, a_r).

In the first test case, 

  * f(1, 2) = max(a_1, a_2) ⋅ min(a_1, a_2) = max(2, 4) ⋅ min(2, 4) = 4 ⋅ 2 = 8. 
  * f(1, 3) = max(a_1, a_2, a_3) ⋅ min(a_1, a_2, a_3) = max(2, 4, 3) ⋅ min(2, 4, 3) = 4 ⋅ 2 = 8. 
  * f(2, 3) = max(a_2, a_3) ⋅ min(a_2, a_3) = max(4, 3) ⋅ min(4, 3) = 4 ⋅ 3 = 12. 


So the maximum is f(2, 3) = 12.

In the second test case, the maximum is f(1, 2) = f(1, 3) = f(2, 3) = 6.
Solve the task in PYTHON3.

Give me a Python code to find the maximum value of max(a_l, a_{l + 1}, …, a_r) ⋅ min(a_l, a_{l + 1}, …, a_r) over all pairs (l, r) of integers for which 1 ≤ l < r ≤ n?
assistant
#Here is Python code to find the maximum value of max(a_l, a_{l + 1}, …, a_r) ⋅ min(a_l, a_{l + 1}, …, a_r) over all pairs (l, r) of integers for which 1 ≤ l < r ≤ n.

# import sys
# # from sortedcontainers import SortedList
# input = sys.stdin.readline

 
# from bisect import bisect_left, bisect_right, insort
# from collections import Sequence, MutableSequence
# from itertools import chain, repeat, starmap
# from math import log
# from operator import add, eq, ne, gt, ge, lt, le, iadd
# from textwrap import dedent
 
# ###############################################################################
# # BEGIN Python 2/3 Shims
# ###############################################################################
 
# from functools import wraps
# from sys import hexversion
 
# if hexversion < 0x03000000:
#     from itertools import imap as map  # pylint: disable=redefined-builtin
#     from itertools import izip as zip  # pylint: disable=redefined-builtin
#     try:
#         from thread import get_ident
#     except ImportError:
#         from dummy_thread import get_ident
# else:
#     from functools import reduce
#     try:
#         from _thread import get_ident
#     except ImportError:
#         from _dummy_thread import get_ident
 
 
# def recursive_repr(fillvalue='...'):
#     "Decorator to make a repr function return fillvalue for a recursive call."
#     # pylint: disable=missing-docstring
#     # Copied from reprlib in Python 3
#     # https://hg.python.org/cpython/file/3.6/Lib/reprlib.py
 
#     def decorating_function(user_function):
#         repr_running = set()
 
#         @wraps(user_function)
#         def wrapper(self):
#             key = id(self), get_ident()
#             if key in repr_running:
#                 return fillvalue
#             repr_running.add(key)
#             try:
#                 result = user_function(self)
#             finally:
#                 repr_running.discard(key)
#             return result
 
#         return wrapper
 
#     return decorating_function
 
# ###############################################################################
# # END Python 2/3 Shims
#...