B"Andrew has n piles with stones. The i -th pile contains a_i stones. He wants to make his table clean so he decided to put every stone either to the 1 -st or the n -th pile. Andrew can perform the following operation any number of times: choose 3 indices 1 <= i < j < k <= n , such that the j -th pile contains at least 2 stones, then he takes 2 stones from the pile j and puts one stone into pile i and one stone into pile k . Tell Andrew what is the minimum number of operations needed to move all the stones to piles 1 and n , or determine if it's impossible. The input contains several test cases. The first line contains one integer t ( 1 <= q t <= q 10 ,000 ) -- the number of test cases. The first line for each test case contains one integer n ( 3 <= q n <= q 10^5 ) -- the length of the array. The second line contains a sequence of integers a_1, a_2, ldots, a_n ( 1 <= q a_i <= q 10^9 ) -- the array elements. It is guaranteed that the sum of the values n over all test cases does not exceed 10^5 . For each test case print the minimum number of operations needed to move stones to piles 1 and n , or print -1 if it's impossible. In the first test case, it is optimal to do the following: In the second test case, it's impossible to put all stones into piles with numbers 1 and 3 : In the third test case, it's optimal to do the following: In the fourth test case, it's impossible to do any operation, and the array doesn't satisfy the statement, so the answer is -1 . "...