Interesting Subarray

For an array a of integers let's denote its maximal element as max(a), and minimal as min(a). We will call an array a of k integers interesting if max(a) - min(a) ≥ k. For example, array [1, 3, 4, 3] isn't interesting as max(a) - min(a) = 4 - 1 = 3 < 4 while array [7, 3, 0, 4, 3] is as max(a) - min(a) = 7 - 0 = 7 ≥ 5.

You are given an array a of n integers. Find some interesting nonempty subarray of a, or tell that it doesn't exist.

An array b is a subarray of an array a if b can be obtained from a by deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end. In particular, an array is a subarray of itself.

Input

The first line contains integer number t (1 ≤ t ≤ 10 000). Then t test cases follow.

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

The second line of each test case contains n integers a_1, a_2, ..., a_n (0≤ a_i ≤ 10^9) — the elements of the array.

It is guaranteed that the sum of n over all test cases does not exceed 2 ⋅ 10^5.

Output

For each test case, output "NO" in a separate line if there is no interesting nonempty subarray in a.

Otherwise, output "YES" in a separate line. In the next line, output two integers l and r (1≤ l ≤ r ≤ n) — bounds of the chosen subarray. If there are multiple answers, print any.

You can print each letter in any case (upper or lower).

Example

Input

3 5 1 2 3 4 5 4 2 0 1 9 2 2019 2020

Output

NO YES 1 4 NO

Note

In the second test case of the example, one of the interesting subarrays is a = [2, 0, 1, 9]: max(a) - min(a) = 9 - 0 = 9 ≥ 4.

inputFormat

Input

The first line contains integer number t (1 ≤ t ≤ 10 000). Then t test cases follow.

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

The second line of each test case contains n integers a_1, a_2, ..., a_n (0≤ a_i ≤ 10^9) — the elements of the array.

It is guaranteed that the sum of n over all test cases does not exceed 2 ⋅ 10^5.

outputFormat

Output

For each test case, output "NO" in a separate line if there is no interesting nonempty subarray in a.

Otherwise, output "YES" in a separate line. In the next line, output two integers l and r (1≤ l ≤ r ≤ n) — bounds of the chosen subarray. If there are multiple answers, print any.

You can print each letter in any case (upper or lower).

Example

Input

3 5 1 2 3 4 5 4 2 0 1 9 2 2019 2020

Output

NO YES 1 4 NO

Note

In the second test case of the example, one of the interesting subarrays is a = [2, 0, 1, 9]: max(a) - min(a) = 9 - 0 = 9 ≥ 4.

样例

3
5
1 2 3 4 5
4
2 0 1 9
2
2019 2020

NO
YES
1 2
NO

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