Optimal Reduction

1000ms

262144K

Description:

Consider an array $$$a$$$ of $$$n$$$ positive integers.

You may perform the following operation:

select two indices $$$l$$$ and $$$r$$$ ($$$1 \leq l \leq r \leq n$$$), then
decrease all elements $$$a_l, a_{l + 1}, \dots, a_r$$$ by $$$1$$$.

Let's call $$$f(a)$$$ the minimum number of operations needed to change array $$$a$$$ into an array of $$$n$$$ zeros.

Determine if for all permutations$$$^\dagger$$$ $$$b$$$ of $$$a$$$, $$$f(a) \leq f(b)$$$ is true.

$$$^\dagger$$$ An array $$$b$$$ is a permutation of an array $$$a$$$ if $$$b$$$ consists of the elements of $$$a$$$ in arbitrary order. For example, $$$[4,2,3,4]$$$ is a permutation of $$$[3,2,4,4]$$$ while $$$[1,2,2]$$$ is not a permutation of $$$[1,2,3]$$$.

Input:

The first line contains a single integer $$$t$$$ ($$$1 \leq t \leq 10^4$$$) — the number of test cases.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \leq n \leq 10^5$$$) — the length of the array $$$a$$$.

The second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 10^9$$$) — description of the array $$$a$$$.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$10^5$$$.

Output:

For each test case, print "YES" (without quotes) if for all permutations $$$b$$$ of $$$a$$$, $$$f(a) \leq f(b)$$$ is true, and "NO" (without quotes) otherwise.

You can output "YES" and "NO" in any case (for example, strings "yEs", "yes" and "Yes" will be recognized as a positive response).

Sample Input:

Sample Output:

YES
YES
NO

Note:

In the first test case, we can change all elements to $$$0$$$ in $$$5$$$ operations. It can be shown that no permutation of $$$[2, 3, 5, 4]$$$ requires less than $$$5$$$ operations to change all elements to $$$0$$$.

In the third test case, we need $$$5$$$ operations to change all elements to $$$0$$$, while $$$[2, 3, 3, 1]$$$ only needs $$$3$$$ operations.

Informação

Provedor Codeforces

Código CF1713B