Problem: You're given an array a_1, …, a_n of n non-negative integers.

Let's call it sharpened if and only if there exists an integer 1 ≤ k ≤ n such that a_1 < a_2 < … < a_k and a_k > a_{k+1} > … > a_n. In particular, any strictly increasing or strictly decreasing array is sharpened. For example:

  * The arrays [4], [0, 1], [12, 10, 8] and [3, 11, 15, 9, 7, 4] are sharpened; 
  * The arrays [2, 8, 2, 8, 6, 5], [0, 1, 1, 0] and [2, 5, 6, 9, 8, 8] are not sharpened. 



You can do the following operation as many times as you want: choose any strictly positive element of the array, and decrease it by one. Formally, you can choose any i (1 ≤ i ≤ n) such that a_i>0 and assign a_i := a_i - 1.

Tell if it's possible to make the given array sharpened using some number (possibly zero) of these operations.

Input

The input consists of multiple test cases. The first line contains a single integer t (1 ≤ t ≤ 15\ 000) — the number of test cases. The description of the test cases follows.

The first line of each test case contains a single integer n (1 ≤ n ≤ 3 ⋅ 10^5).

The second line of each test case contains a sequence of n non-negative integers a_1, …, a_n (0 ≤ a_i ≤ 10^9).

It is guaranteed that the sum of n over all test cases does not exceed 3 ⋅ 10^5.

Output

For each test case, output a single line containing "Yes" (without quotes) if it's possible to make the given array sharpened using the described operations, or "No" (without quotes) otherwise.

Example

Input


10
1
248618
3
12 10 8
6
100 11 15 9 7 8
4
0 1 1 0
2
0 0
2
0 1
2
1 0
2
1 1
3
0 1 0
3
1 0 1


Output


Yes
Yes
Yes
No
No
Yes
Yes
Yes
Yes
No

Note

In the first and the second test case of the first test, the given array is already sharpened.

In the third test case of the first test, we can transform the array into [3, 11, 15, 9, 7, 4] (decrease the first element 97 times and decrease the last element 4 times). It is sharpened because 3 < 11 < 15 and 15 > 9 > 7 > 4.

In the fourth test case of the first test, it's impossible to make the given array sharpened.

Solution (in JAVA):

Solution:
import static java.lang.Integer.parseInt;
import static java.lang.Long.parseLong;
import static java.lang.Short.parseShort;
import static java.lang.Byte.parseByte;
import java.io.*;
import java.util.*;

public class Contest {

    static int nextInt() throws IOException {
        return parseInt(next());
    }

    static long nextLong() throws IOException {
        return parseLong(next());
    }

    static short nextShort() throws IOException {
        return parseShort(next());
    }

    static byte nextByte() throws IOException {
        return parseByte(next());
    }

    static String next() throws IOException {
        while (tok == null || !tok.hasMoreTokens())
            tok = new StringTokenizer(in.readLine());
        return tok.nextToken();
    }

    static String nextLine() throws IOException {
        return in.readLine();
    }

    private static BufferedReader in;
    private static StringTokenizer tok;
    private static PrintWriter out = new PrintWriter(System.out);
    private static Utilities doThis = new Utilities(out);
    private static MyMath doMath = new MyMath();
    private static NextPermutation permute = new NextPermutation();

    public static void main(String[] args) throws Exception {
        in = new BufferedReader(new InputStreamReader(System.in));

        /*--------------------SolutionStarted-------------------*/
        solve();
        /*--------------------SolutionEnded--------------------*/

        in.close();
        out.close();
    }


    static int n, m, k,
            count = 0, length = 0, sum = 0,
            q, t,
            idx, temp;
    static char[] s, s1;
    static int max = Integer.MIN_VALUE, min = Integer.MAX_VALUE;
    static long lMax = Long.MAX_VALUE, lMin = Long.MIN_VALUE, lSum = 0, lCount;
    static int[] nums;
    static boolean flag;
    static List<Integer> permutation;
    static boolean chosen[];

    static void solve() throws IOException {
        t = nextInt();
        whl:
        while (t-- > 0) {
            n = nextInt();
            nums = new int[n];
            for (int i = 0; i < n; i++)
                nums[i] = nextInt();
            int start = -1, end = n;
            temp = n - 1;
            for (int i = 0; i < n; i++) {
                if (nums[i] < i)
                    break;
                start = i;
            }
            for (int i = temp; i >= 0; i--) {
                if (nums[i] < (temp - i))
                    break;
                end = i;
            }
            if(end<=start)
                doThis.yes();
            else doThis.no();
        }
    }
}
class Pair implements Comparable<Pair>{
    int k,v;
    boolean taken;
    Pair(int k,int v){
        this.k = k;
        this.v =v;
    }

    @Override
    public int compareTo(Pair o) {
        return v-o.v;
    }
}
class CharPair{
    char ch;
    int value;
    CharPair(char c, int v){
        ch =c; value=v;
    }
    char get(){
        return ch;
    }
}
class IntPair implements Comparable<IntPair> {
    int key, value;
    IntPair(int key, int value) {
        this.key =  key;
        this.value = value;
    }

    @Override
    public int compareTo(IntPair o) {
        if (value == o.value)
            return key - o.key;
        return value - o.value;
    }

    public String toString() {
        return key + " " + value;
    }
}
class BooleanPair {
    boolean key, value;

    BooleanPair() {
    }

    BooleanPair(boolean key, boolean value) {
        this.key = key;
        this.value = value;
    }
}
class Utilities {
    PrintWriter out;
    Utilities(PrintWriter out){
        this.out = out;
    }
    //int arrays start
    int lowerBound(int[] arr, int low, int high, int element) {
        int middle;
        while (low < high) {
            middle = low + (high - low) / 2;
            if (element > arr[middle])
                low = middle + 1;
            else
                high = middle;
        }
        if (arr[low] < element)
            return -1;
        return low;
    }

    int upperBound(int[] arr, int low, int high, int element) {
        int middle;
        while (low < high) {
            middle = low + (high - low) / 2;
            if (arr[middle] > element)
                high = middle;
            else
                low = middle + 1;
        }
        if (arr[low] <= element)
            return -1;
        return low;
    }
    //int arrays end
    //long arrays start
    int lowerBound(long[] arr, int low, int high, long element) {
        int middle;
        while (low < high) {
            middle = low + (high - low) / 2;
            if (element > arr[middle])
                low = middle + 1;
            else
                high = middle;
        }
        if (arr[low] < element)
            return -1;
        return low;
    }

    int upperBound(long[] arr, int low, int high, long element) {
        int middle;
        while (low < high) {
            middle = low + (high - low) / 2;
            if (arr[middle] > element)
                high = middle;
            else
                low = middle + 1;
        }
        if (arr[low] <= element)
            return -1;
        return low;
    }
    //long arrays end
    //double arrays start
    int lowerBound(double[] arr, int low, int high, double element) {
        int middle;
        while (low < high) {
            middle = low + (high - low) / 2;
            if (element > arr[middle])
                low = middle + 1;
            else
                high = middle;
        }
        if (arr[low] < element)
            return -1;
        return low;
    }

    int upperBound(double[] arr, int low, int high, double element) {
        int middle;
        while (low < high) {
            middle = low + (high - low) / 2;
            if (arr[middle] > element)
                high = middle;
            else
                low = middle + 1;
        }
        if (arr[low] <= element)
            return -1;
        return low;
    }
    //double arrays end
    int arrUp(int [][]arr,int i, int j){
        if(i==0)
            return Integer.MIN_VALUE;
        return arr[i-1][j];
    }
    int arrDown(int [][]arr,int i, int j){
        if(i==arr.length-1)
            return Integer.MIN_VALUE;
        return arr[i+1][j];
    }
    int arrLeft(int [][]arr,int i, int j){
        if(j==0)
            return Integer.MIN_VALUE;
        return arr[i][j-1];
    }
    int arrRight(int [][]arr,int i, int j){
        if(j==arr[i].length-1)
            return Integer.MIN_VALUE;
        return arr[i][j+1];
    }
    int count(char[] s, char c){
        int count = 0;
        for (int i = 0; i < s.length; i++) {
            if (s[i]==c)
                count++;
        }
        return count;
    }
    void swap(char[] s, int a,int b){
        char temp =s[b];
        s[b]= s[a];
        s[a] = temp;
    }
    boolean odd(int a){
        return (a&1)==1;
    }
    boolean even(int a){
        return (a&1)==0;
    }
    void yes(){
        out.println("YES");
    }
    void no() {
        out.println("NO");
    }
    void bad(){
        out.println(-1);
    }
    void printBinary(int num){
        out.println(Integer.toBinaryString(num));
    }
    void printArr(int arr[]){
        for (int i = 0; i <arr.length ; i++) {
            out.print(arr[i]+" ");
        }
    }
}
class MyMath {
    boolean isCoPrime(int a, int b) {
        return gcd(a, b) == 1;
    }

    int gcd(int a, int b) {
        if (a == 0)
            return b;
        while (b != 0)
            if (a > b)
                a = a - b;
            else
                b = b - a;
        return a;
    }

    int log2(int x) {
        return (int) (Math.log(x) / Math.log(2));
    }
    boolean[] sieveOfEratosthenes(int n)
    {
        // Create a boolean array "primes[0..n]" and initialize
        // all entries it as true. A value in primes[i] will
        // finally be false if i is Not a primes, else true.
        boolean primes[] = new boolean[n+1];
        for(int i=0;i<n;i++)
            primes[i] = true;

        for(int p = 2; p*p <=n; p++)
        {
            // If primes[p] is not changed, then it is a primes
            if(primes[p])
            {
                // Update all multiples of p
                for(int i = p*p; i <= n; i += p)
                    primes[i] = false;
            }
        }
        return primes;
    }
}
class NextPermutation {

    // Function to swap the data
    // present in the left and right indices
    private int[] swap(int data[], int left, int right) {

        // Swap the data
        int temp = data[left];
        data[left] = data[right];
        data[right] = temp;

        // Return the updated array
        return data;
    }

    // Function to reverse the sub-array
    // starting from left to the right
    // both inclusive
    private int[] reverse(int data[], int left, int right) {

        // Reverse the sub-array
        while (left < right) {
            int temp = data[left];
            data[left++] = data[right];
            data[right--] = temp;
        }

        // Return the updated array
        return data;
    }

    // Function to find the next permutation
    // of the given integer array
    boolean findNextPermutation(int data[]) {

        // If the given data-set is empty
        // or contains only one element
        // next_permutation is not possible
        if (data.length <= 1)
            return false;

        int last = data.length - 2;

        // find the longest non-increasing suffix
        // and find the pivot
        while (last >= 0) {
            if (data[last] < data[last + 1]) {
                break;
            }
            last--;
        }

        // If there is no increasing pair
        // there is no higher order permutation
        if (last < 0)
            return false;

        int nextGreater = data.length - 1;

        // Find the rightmost successor to the pivot
        for (int i = data.length - 1; i > last; i--) {
            if (data[i] > data[last]) {
                nextGreater = i;
                break;
            }
        }

        // Swap the successor and the pivot
        data = swap(data, nextGreater, last);

        // Reverse the suffix
        data = reverse(data, last + 1, data.length - 1);

        // Return true as the next_permutation is done
        return true;
    }
}