Let's say you are standing on the XY-plane at point (0, 0) and you want to reach point (n, n).

You can move only in two directions: 

  * to the right, i. e. horizontally and in the direction that increase your x coordinate, 
  * or up, i. e. vertically and in the direction that increase your y coordinate. 



In other words, your path will have the following structure: 

  * initially, you choose to go to the right or up; 
  * then you go some positive integer distance in the chosen direction (distances can be chosen independently); 
  * after that you change your direction (from right to up, or from up to right) and repeat the process. 



You don't like to change your direction too much, so you will make no more than n - 1 direction changes.

As a result, your path will be a polygonal chain from (0, 0) to (n, n), consisting of at most n line segments where each segment has positive integer length and vertical and horizontal segments alternate.

Not all paths are equal. You have n integers c_1, c_2, ..., c_n where c_i is the cost of the i-th segment.

Using these costs we can define the cost of the path as the sum of lengths of the segments of this path multiplied by their cost, i. e. if the path consists of k segments (k ≤ n), then the cost of the path is equal to ∑_{i=1}^{k}{c_i ⋅ length_i} (segments are numbered from 1 to k in the order they are in the path).

Find the path of the minimum cost and print its cost.

Input

The first line contains the single integer t (1 ≤ t ≤ 1000) — the number of test cases.

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

The second line of each test case contains n integers c_1, c_2, ..., c_n (1 ≤ c_i ≤ 10^9) — the costs of each segment.

It's guaranteed that the total sum of n doesn't exceed 10^5.

Output

For each test case, print the minimum possible cost of the path from (0, 0) to (n, n) consisting of at most n alternating segments.

Example

Input


3
2
13 88
3
2 3 1
5
4 3 2 1 4


Output


202
13
19

Note

In the first test case, to reach (2, 2) you need to make at least one turn, so your path will consist of exactly 2 segments: one horizontal of length 2 and one vertical of length 2. The cost of the path will be equal to 2 ⋅ c_1 + 2 ⋅ c_2 = 26 + 176 = 202.

In the second test case, one of the optimal paths consists of 3 segments: the first segment of length 1, the second segment of length 3 and the third segment of length 2.

The cost of the path is 1 ⋅ 2 + 3 ⋅ 3 + 2 ⋅ 1 = 13.

In the third test case, one of the optimal paths consists of 4 segments: the first segment of length 1, the second one — 1, the third one — 4, the fourth one — 4. The cost of the path is 1 ⋅ 4 + 1 ⋅ 3 + 4 ⋅ 2 + 4 ⋅ 1 = 19.
import java.util.*;
import java.util.Map.Entry;


import java.io.*;
import java.math.*;
import static java.util.stream.Collectors.*;
import static java.util.Map.Entry.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Hey
{
	public static void main (String[] args) throws IOException
	{
		final long mod=(long) (1e9+7);  
		
		Reader s=new Reader();
		  PrintWriter pt=new PrintWriter(System.out);
//		  BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		  int T=s.nextInt();
//		  int T=Integer.parseInt(br.readLine());
//		  int T=1;
		  while(T-->0)
		  {
			  int n=s.nextInt();
			  int c[]=new int[n];
			  for(int i=0;i<n;i++) {
				  c[i]=s.nextInt();
			  }
			  long mo[]=new long[n];
			  long me[]=new long[n];
			  mo[0]=-1;
			  me[0]=-1;
			  mo[1]=c[0];
			  me[1]=c[1];
			  long so[]=new long[n];
			  long se[]=new long[n];
			  so[1]=c[0];
			  se[1]=c[1];
			  for(int i=2;i<n;i++) {
				  if(i%2==0) {
					  mo[i]=Math.min(c[i], mo[i-1]);
					  me[i]=me[i-1];
					  so[i]=so[i-1]+c[i];
					  se[i]=se[i-1];
				  }
				  else {
					  mo[i]=mo[i-1];
					  me[i]=Math.min(c[i], me[i-1]);
					  so[i]=so[i-1];
					  se[i]=se[i-1]+c[i];
				  }
			  }
			  
//			  pa(mo);
//			  pa(me);
//			  pa(so);
//			  pa(se);
			  long min=Long.MAX_VALUE;
			  for(int i=1;i<n;i++) {
				  long k1=0, k2=0;
				  if(i%2==1) {
					  k1=i/2+1;
					  k2=i/2+1;
				  }
				  else {
					  k2=i/2;
					  k1=k2+1;
				  }
				  min=Math.min((n-k1)*mo[i]+so[i]+(n-k2)*me[i]+se[i], min);
			  }
			  pt.println(min);
		  }
		  pt.close();
	}
	
	static boolean isSorted(int arr[], int n) {
		for(int i=1;i<n;i++) {
			if(arr[i]>=arr[i-1]==false) {
				return false;
			}
		}
		return true;
	}
	
	static int setBit(int S, int j) { return S | 1 << j; }

	static int clearBit(int S, int j) { return S & ~(1 << j); }

	static int toggleBit(int S, int j) { return S ^ 1 << j; }

	static boolean isOn(int S, int j) { return (S & 1 << j) != 0; }

	static int turnOnLastZero(int S) { return S | S + 1; }
	
	static int turnOnLastConsecutiveZeroes(int S) { return S | S - 1; }
	
	static int turnOffLastBit(int S) { return S & S - 1; }
	
	static int turnOffLastConsecutiveBits(int S) { return S & S + 1; }

	static int lowBit(int S) { return S & -S; }

	static int setAll(int N) { return (1 << N) - 1; }

	static int modulo(int S, int N) { return (S & N - 1); }		 //S%N, N is a power of 2

	static boolean isPowerOfTwo(int S) { return (S & S - 1) == 0; }
	
	static boolean isWithin(long x, long y, long d, long k) {
		return x*k*x*k + y*k*y*k <= d*d;
	}
	
	static long modFact(long n, 
            long p) 
	{ 
		if (n >= p) 
		 return 0; 
		
		long result = 1; 
		for (int i = 1; i <= n; i++) 
		 result = (result * i) % p; 
		
		return result; 
	} 
	static int sum(int[] arr, int n)
	{
	    int inc[]=new int[n+1];
	    int dec[]=new int[n+1];
	    inc[0] = arr[0];
	    dec[0] = arr[0];

	    for (int i = 1; i < n; i++) {
	        for (int j = 0; j < i; j++) {
	            if (arr[j] > arr[i]) {
	                dec[i] = max(dec[i], inc[j] + arr[i]);
	            }
	            else if (arr[i] > arr[j]) {
	                inc[i] = max(inc[i], dec[j] + arr[i]);
	            }
	        }
	    }
	    return max(inc[n - 1], dec[n - 1]);
	}
	static long nc2(long a) {
		return a*(a-1)/2;
	}
	public static int numberOfprimeFactors(int n) 
    { 
        // Print the number of 2s that divide n 
		HashSet<Integer> hs = new HashSet<Integer>();
        while (n%2==0) 
        { 
            hs.add(2);
            n /= 2; 
        } 
  
        // n must be odd at this point.  So we can 
        // skip one element (Note i = i +2) 
        for (int i = 3; i <= Math.sqrt(n); i+= 2) 
        { 
            // While i divides n, print i and divide n 
            while (n%i == 0) 
            { 
                hs.add(i);
                n /= i; 
            } 
        } 
  
        // This condition is to handle the case whien 
        // n is a prime number greater than 2 
        if (n > 2) 
            hs.add(n);
        return hs.size();
    } 
	static int gcd(int a, int b) 
    { 
      if (b == 0) 
        return a; 
      return gcd(b, a % b);  
    } 




	

	static void reverse(int arr[],int start, int end) 
	{ 
		int temp; 
		   
		while (start < end) 
		{ 
		    temp = arr[start];  
		    arr[start] = arr[end]; 
		    arr[end] = temp; 
		    start++; 
		    end--; 
		}  
	}  
	static void reverse(long arr[],int start, int end) 
	{ 
		long temp; 
		   
		while (start < end) 
		{ 
		    temp = arr[start];  
		    arr[start] = arr[end]; 
		    arr[end] = temp; 
		    start++; 
		    end--; 
		}  
	}  
	static boolean isPrime(long n) 
    { 
        // Corner cases 
        if (n <= 1) return false; 
        if (n <= 3) return true; 
      
        // This is checked so that we can skip  
        // middle five numbers in below loop 
        if (n % 2 == 0 || n % 3 == 0) return false; 
      
        for (int i = 5; i * i <= n; i = i + 6) 
            if (n % i == 0 || n % (i + 2) == 0) 
            return false; 
      
        return true; 
    } 
	static int p2(int n) {
		int k=0;
		while(n>1) {
			if(n%2!=0)
				return k;
			n/=2;
			k++;
		}
		return k;
	}
	static boolean isp2(int n) {
		while(n>1) {
			if(n%2==1)
				return false;
			n/=2;
		}
		return true;
	}
	static int binarySearch(int arr[], int first, int last, int key){  
		   int mid = (first + last)/2;  
		   while( first <= last ){  
		      if ( arr[mid] < key ){  
		        first = mid + 1;     
		      }else if ( arr[mid] == key ){  
		        return mid;  
		      }else{  
		         last = mid - 1;  
		      }  
		      mid = (first + last)/2;  
		   }  
		   return -1;
		 }  

	static void print(int a[][]) {
		for(int i=0;i<a.length;i++)
		{
			for(int j=0;j<a[0].length;j++)
				System.out.print(a[i][j]+" ");
			System.out.println();
		}
	}
	static int max (int x, int y) {
		return (x > y)? x : y;
	} 
	static int search(Pair[] p, Pair pair) {
		int l=0, r=p.length;
		while (l <= r) { 
	        int m = l + (r - l) / 2;
	        if (p[m].compareTo(pair)==0) 
	            return m; 
	        if (p[m].compareTo(pair)<0) 
	            l = m + 1; 
	        else
	            r = m - 1;
	    }
	    return -1;
	}
	static void pa(int a[])
	{
		for(int i=0;i<a.length;i++)
			System.out.print(a[i]+" ");
		System.out.println();
		
	}
	static void pa(long a[])
	{
		for(int i=0;i<a.length;i++)
			System.out.print(a[i]+" ");
		System.out.println();
		
	}
	static void reverseArray(int arr[], 
            int start, int end) 
	{ 
		int temp; 
		   
		while (start < end) 
		{ 
		    temp = arr[start];  
		    arr[start] = arr[end]; 
		    arr[end] = temp; 
		    start++; 
		    end--; 
		}  
	}     
	static boolean isPalindrome(String s) {
		int l=s.length();
		for(int i=0;i<l/2;i++)
		{
			if(s.charAt(i)!=s.charAt(l-i-1))
				return false;
		}
		return true;
	}
	static long nc2(long n, long m) {
		return (n*(n-1)/2)%m;
	}
	static long c(long a) {
		return a*(a+1)/2;
	}
	static int next(int[] arr, int target)  
    {  
        int start = 0, end = arr.length - 1;  
    
        int ans = -1;  
        while (start <= end) {  
            int mid = (start + end) / 2;  
    
            // Move to right side if target is  
            // greater.  
            if (arr[mid] < target) {  
                start = mid + 1;  
            }  
    
            // Move left side.  
            else {  
                ans = mid;  
                end = mid - 1;  
            }  
        }  
        return ans;  
    }  

	static long power(long x, long y, long p) 
    { 
        long res = 1; 
        x = x % p; 
                      
        while (y > 0) 
        { 
            if (y % 2 == 1) 
                res = (res * x) % p; 
            y = y >> 1;
            x = (x * x) % p; 
        } 
        return  res; 
    } 
    static long modInverse(long n, long p) 
    { 
        return power(n, p-2, p); 
    } 
    static long nCrModP(long n, long r, 
                                    long p) 
    { 
        if(r>n)
        	return 0;
    	if (r == 0) 
            return 1; 
        long[] fac = new long[(int) (n+1)]; 
        fac[0] = 1; 
        for (int i = 1 ;i <= n; i++) 
            fac[i] = fac[i-1] * i % p; 
        return (fac[(int) n]* modInverse(fac[(int) r], p) 
                % p * modInverse(fac[(int) (n-r)], p) 
                                    % p) % p; 
    } 
	static String reverse(String str)
	{
		return new StringBuffer(str).reverse().toString();
	}



	static long fastpow(long x, long y, long m)  
    { 
        if (y == 0) 
            return 1; 
          
        long p = fastpow(x, y / 2, m) % m; 
        p = (p * p) % m; 
      
        if (y % 2 == 0) 
            return p; 
        else
            return (x * p) % m; 
    } 
	
	static boolean isPerfectSquare(long l)
	{
		return Math.pow((long)Math.sqrt(l),2)==l;
	}
	
	
	static void merge(long[] arr, int l, int m, int r) 
    { 
        // Find sizes of two subarrays to be merged 
        int n1 = m - l + 1; 
        int n2 = r - m; 
  
        /* Create temp arrays */
        long L[] = new long [n1]; 
        long R[] = new long [n2]; 
  
        /*Copy data to temp arrays*/
        for (int i=0; i<n1; ++i) 
            L[i] = arr[l + i]; 
        for (int j=0; j<n2; ++j) 
            R[j] = arr[m + 1+ j]; 
  
  
        /* Merge the temp arrays */
  
        // Initial indexes of first and second subarrays 
        int i = 0, j = 0; 
  
        // Initial index of merged subarry array 
        int k = l; 
        while (i < n1 && j < n2) 
        { 
            if (L[i] <= R[j]) 
            { 
                arr[k] = L[i]; 
                i++; 
            } 
            else
            { 
                arr[k] = R[j]; 
                j++; 
            } 
            k++; 
        } 
  
        /* Copy remaining elements of L[] if any */
        while (i < n1) 
        { 
            arr[k] = L[i]; 
            i++; 
            k++; 
        } 
  
        /* Copy remaining elements of R[] if any */
        while (j < n2) 
        { 
            arr[k] = R[j]; 
            j++; 
            k++; 
        } 
    } 
  
    // Main function that sorts arr[l..r] using 
    // merge() 
    static void sort(int arr[], int l, int r) 
    { 
        if (l < r) 
        { 
            // Find the middle point 
            int m = (l+r)/2; 
  
            // Sort first and second halves 
            sort(arr, l, m); 
            sort(arr , m+1, r); 
  
            // Merge the sorted halves 
            merge(arr, l, m, r); 
        } 
    } 
	static void merge(int arr[], int l, int m, int r) 
    { 
        // Find sizes of two subarrays to be merged 
        int n1 = m - l + 1; 
        int n2 = r - m; 
  
        /* Create temp arrays */
        int L[] = new int [n1]; 
        int R[] = new int [n2]; 
  
        /*Copy data to temp arrays*/
        for (int i=0; i<n1; ++i) 
            L[i] = arr[l + i]; 
        for (int j=0; j<n2; ++j) 
            R[j] = arr[m + 1+ j]; 
  
  
        /* Merge the temp arrays */
  
        // Initial indexes of first and second subarrays 
        int i = 0, j = 0; 
  
        // Initial index of merged subarry array 
        int k = l; 
        while (i < n1 && j < n2) 
        { 
            if (L[i] <= R[j]) 
            { 
                arr[k] = L[i]; 
                i++; 
            } 
            else
            { 
                arr[k] = R[j]; 
                j++; 
            } 
            k++; 
        } 
  
        /* Copy remaining elements of L[] if any */
        while (i < n1) 
        { 
            arr[k] = L[i]; 
            i++; 
            k++; 
        } 
  
        /* Copy remaining elements of R[] if any */
        while (j < n2) 
        { 
            arr[k] = R[j]; 
            j++; 
            k++; 
        } 
    } 
  
    // Main function that sorts arr[l..r] using 
    // merge() 
    static void sort(long arr[], int l, int r) 
    { 
        if (l < r) 
        { 
            // Find the middle point 
            int m = (l+r)/2; 
  
            // Sort first and second halves 
            sort(arr, l, m); 
            sort(arr , m+1, r); 
  
            // Merge the sorted halves 
            merge(arr, l, m, r); 
        } 
    } 
    static class Pair implements Comparable<Pair>{
        int a;
        int b;
        Pair(int a,int b){
            this.a=a;
 
            this.b=b;
        }   
        public int compareTo(Pair p){
            if(a>p.a)
                return 1;
            if(a==p.a)
                return (b-p.b);
            return -1;
        }
    }
	static class Reader 
    { 
        final private int BUFFER_SIZE = 1 << 16; 
        private DataInputStream din; 
        private byte[] buffer; 
        private int bufferPointer, bytesRead; 
  
        public Reader() 
        { 
            din = new DataInputStream(System.in); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        } 
  
        public Reader(String file_name) throws IOException 
        { 
            din = new DataInputStream(new FileInputStream(file_name)); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        } 
  
        public String readLine() throws IOException 
        { 
            byte[] buf = new byte[128]; // line length 
            int cnt = 0, c; 
            while ((c = read()) != -1) 
            { 
                if (c == '\n') 
                    break; 
                buf[cnt++] = (byte) c; 
            } 
            return new String(buf, 0, cnt); 
        } 
  
        public int nextInt() throws IOException 
        { 
            int ret = 0; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
            do
            { 
                ret = ret * 10 + c - '0'; 
            }  while ((c = read()) >= '0' && c <= '9'); 
  
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        public long nextLong() throws IOException 
        { 
            long ret = 0; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
            do { 
                ret = ret * 10 + c - '0'; 
            } 
            while ((c = read()) >= '0' && c <= '9'); 
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        public double nextDouble() throws IOException 
        { 
            double ret = 0, div = 1; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
  
            do { 
                ret = ret * 10 + c - '0'; 
            } 
            while ((c = read()) >= '0' && c <= '9'); 
  
            if (c == '.') 
            { 
                while ((c = read()) >= '0' && c <= '9') 
                { 
                    ret += (c - '0') / (div *= 10); 
                } 
            } 
  
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        private void fillBuffer() throws IOException 
        { 
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE); 
            if (bytesRead == -1) 
                buffer[0] = -1; 
        } 
  
        private byte read() throws IOException 
        { 
            if (bufferPointer == bytesRead) 
                fillBuffer(); 
            return buffer[bufferPointer++]; 
        } 
  
        public void close() throws IOException 
        { 
            if (din == null) 
                return; 
            din.close(); 
        } 
    } 
}