As is well known, Nikita loves reading. Today, he made a mess in his room and arranged his books into (n) stacks in a row, numbered from (1) to (n) from left to right. The (i)-th stack contains (a_i) books. This arrangement is called neat if, in every stack except the rightmost one, the number of books is strictly less than in the stack to its right; that is, the array (a) is strictly increasing. Yura wants to make the arrangement neat by performing the following operation any number of times: Choose a stack (i) such that (1 \le i \lt n) and (a_i \gt 1). Take (1) book from the top of stack (i), so (a_i) decreases by (1). Put this book on top of stack (i + 1), so (a_{i+1}) increases by (1). Determine whether Yura can make the arrangement neat . The first line contains a single integer (t) ((1 \le t \le 10^4)) — the number of test cases. The first line of each test case contains a single integer (n) ((1 \le n \le 2 \cdot 10^5)) — the number of stacks. The second line of each test case contains (n) integers (a_i) ((1 \le a_i \le 10^9)) — the initial number of books in each stack. It is guaranteed that the sum of (n) over all test cases does not exceed (2 \cdot 10^5). For each test case, output " YES " if Yura can make the arrangement neat , and " NO " otherwise. You may output each letter in any case (lowercase or uppercase). For example, the strings " yEs ", " yes ", " Yes ", and " YES " will be accepted.