Consider an infinite triangle made up of layers. Let's number the layers, starting from one, from the top of the triangle (from top to bottom). The k-th layer of the triangle contains k points, numbered from left to right. Each point of an infinite triangle is described by a pair of numbers (r, c) (1 ≤ c ≤ r), where r is the number of the layer, and c is the number of the point in the layer. From each point (r, c) there are two directed edges to the points (r+1, c) and (r+1, c+1), but only one of the edges is activated. If r + c is even, then the edge to the point (r+1, c) is activated, otherwise the edge to the point (r+1, c+1) is activated. Look at the picture for a better understanding.

<image> Activated edges are colored in black. Non-activated edges are colored in gray.

From the point (r_1, c_1) it is possible to reach the point (r_2, c_2), if there is a path between them only from activated edges. For example, in the picture above, there is a path from (1, 1) to (3, 2), but there is no path from (2, 1) to (1, 1).

Initially, you are at the point (1, 1). For each turn, you can: 

  * Replace activated edge for point (r, c). That is if the edge to the point (r+1, c) is activated, then instead of it, the edge to the point (r+1, c+1) becomes activated, otherwise if the edge to the point (r+1, c+1), then instead if it, the edge to the point (r+1, c) becomes activated. This action increases the cost of the path by 1; 
  * Move from the current point to another by following the activated edge. This action does not increase the cost of the path. 



You are given a sequence of n points of an infinite triangle (r_1, c_1), (r_2, c_2), …, (r_n, c_n). Find the minimum cost path from (1, 1), passing through all n points in arbitrary order.

Input

The first line contains one integer t (1 ≤ t ≤ 10^4) is the number of test cases. Then t test cases follow.

Each test case begins with a line containing one integer n (1 ≤ n ≤ 2 ⋅ 10^5) is the number of points to visit.

The second line contains n numbers r_1, r_2, …, r_n (1 ≤ r_i ≤ 10^9), where r_i is the number of the layer in which i-th point is located.

The third line contains n numbers c_1, c_2, …, c_n (1 ≤ c_i ≤ r_i), where c_i is the number of the i-th point in the r_i layer.

It is guaranteed that all n points are distinct.

It is guaranteed that there is always at least one way to traverse all n points.

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

Output

For each test case, output the minimum cost of a path passing through all points in the corresponding test case.

Example

Input


4
3
1 4 2
1 3 1
2
2 4
2 3
2
1 1000000000
1 1000000000
4
3 10 5 8
2 5 2 4


Output


0
1
999999999
2
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.InputMismatchException;
import java.util.*;
import java.io.*;
import java.lang.*;
public class Main{
    public static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;
        private BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
     
        public InputReader(InputStream stream) {
            this.stream = stream;
        }
     
        public int read() {
            if (numChars==-1)
                throw new InputMismatchException();
     
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                }
                catch (IOException e) {
                    throw new InputMismatchException();
                }
     
                if(numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }
     
        public String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            }
            catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
        public int nextInt() {
            int c = read();
     
            while(isSpaceChar(c))
                c = read();
     
            int sgn = 1;
     
            if (c == '-') {
                sgn = -1;
                c = read();
            }
     
            int res = 0;
            do {
                if(c<'0'||c>'9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));
     
            return res * sgn;
        }
     
        public long nextLong() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
     
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));
            return res * sgn;
        }
     
        public double nextDouble() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }
     
        public String readString() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            }
            while (!isSpaceChar(c));
     
            return res.toString();
        }
     
        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
     
        public String next() {
            return readString();
        }
     
        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }
 
    static long gcd(long a, long b){
        if (a == 0)
            return b;  
        return gcd(b % a, a);  
    }
    static long lcm(long a, long b)  {
        return (a*b)/gcd(a, b);  
    }
    public static void sortbyColumn(int arr[][], int col) 
    { 
        
        Arrays.sort(arr, new Comparator<int[]>() { 
            
          @Override              
          
          public int compare(final int[] entry1,  
                             final int[] entry2) { 
  
            
            if (entry1[col] > entry2[col]) 
                return 1; 
            else
                return -1; 
          } 
        });  
    } 
    static long func(long a[],int size,int s){
        long max1=a[s];
        long maxc=a[s];
        for(int i=s+1;i<size;i++){
            maxc=Math.max(a[i],maxc+a[i]);
            max1=Math.max(maxc,max1);
        }
        return max1;
    }
    public static class Pair<U extends Comparable<U>, V extends Comparable<V>> implements Comparable<Pair<U, V>> {
        public U x;
        public V y;
    
        public Pair(U x, V y) {
            this.x = x;
            this.y = y;
        }
    
        public int hashCode() {
            return (x == null ? 0 : x.hashCode() * 31) + (y == null ? 0 : y.hashCode());
        }
    
        public boolean equals(Object o) {
            if (this == o)
                return true;
            if (o == null || getClass() != o.getClass())
                return false;
            Pair<U, V> p = (Pair<U, V>) o;
            return (x == null ? p.x == null : x.equals(p.x)) && (y == null ? p.y == null : y.equals(p.y));
        }
    
        public int compareTo(Pair<U, V> b) {
            int cmpU = x.compareTo(b.x);
            return cmpU != 0 ? cmpU : y.compareTo(b.y);
        }
    
        public String toString() {
            return String.format("(%s, %s)", x.toString(), y.toString());
        }
    
    }
    static class MultiSet<U extends Comparable<U>> {
        public int sz = 0;
        public TreeMap<U, Integer> t;
 
        public MultiSet() {
            t = new TreeMap<>();
        }
 
        public void add(U x) {
            t.put(x, t.getOrDefault(x, 0) + 1);
            sz++;
        }
 
        public void remove(U x) {
            if (t.get(x) == 1) t.remove(x);
            else t.put(x, t.get(x) - 1);
            sz--;
        }
 
    }
    static void shuffle(long[] a) {
        Random get = new Random();
        for (int i = 0; i < a.length; i++) {
            int r = get.nextInt(a.length);
            long temp = a[i];
            a[i] = a[r];
            a[r] = temp;
        }
    }
    static long myceil(long a, long b){
        return (a+b-1)/b;
    }
    
    static long C(long n,long r){
        long count=0,temp=n;
        long ans=1;
        long num=n-r+1,div=1;
        while(num<=n){
            ans*=num;
            //ans+=MOD;
            ans%=MOD;
            ans*=mypow(div,MOD-2);
            //ans+=MOD;
            ans%=MOD;
            num++;
            div++;
        }
        
        ans+=MOD;
        return ans%MOD;
    }
    static long fact(long a){
        long i,ans=1;
        for(i=1;i<=a;i++){
            ans*=i;
            ans%=MOD;
        }
        return ans%=MOD;
    }
    static void sieve(int n){
        is_sieve[0]=1;
        is_sieve[1]=1;
        int i,j,k;
        for(i=2;i<n;i++){
            if(is_sieve[i]==0){
                sieve[i]=i;
                tr.add(i);
                for(j=i*i;j<n;j+=i){
                    if(j>n||j<0){
                        break;
                    }
                    is_sieve[j]=1;
                    sieve[j]=i;
                }
            }
        }
    }
    // static void calc(int n){
    //     int i,j;
    //     dp[n-1]=0;
    //     if(n>1)
    //     dp[n-2]=1;
    //     for(i=n-3;i>=0;i--){
    //         long ind=n-i-1;
    //         dp[i]=((ind*(long)mypow(10,ind-1))%MOD+dp[i+1])%MOD;
    //     }
    // }
    static long mypow(long x,long y){
        long temp; 
        if( y == 0) 
            return 1; 
        temp = mypow(x, y/2); 
        if (y%2 == 0) 
            return (temp*temp)%MOD; 
        else
            return ((x*temp)%MOD*(temp)%MOD)%MOD; 
    }
    static long dist[],dp[][];
    static int visited[],isit[];
    static ArrayList<Integer> adj[],li;
    //static int dp[][][];
    static int MOD=1000000007,max=0;
    static char ch[];
    static int[] sieve,is_sieve;
    static TreeSet<Integer> tr;
    
    static int calcdist(int r1,int c1,int r2,int c2){
        if(r2-r1==c2-c1){
            return isRight(r1,c1)?0:r2-r1;
        }
        
        r2-=r1-1;
        c2-=c1-1;
        if(isLeft(r1,c1)){
            return (r2-c2)/2;
        }else{
            return (r2-c2+1)/2;
        }
    }
    
    static boolean isLeft(int r,int c){
        if((r+c)%2==0){
            return true;
        }
        return false;
    }
    
    static boolean isRight(int r,int c){
        if((r+c)%2!=0){
            return true;
        }
        return false;
    }
    
    public static void main(String args[]){
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter w = new PrintWriter(outputStream);
        int t,i,j,tno=0,tte;
        
        t=in.nextInt();
        //t=1;
        //tte=t;
        
        while(t-->0){
            int n=in.nextInt();
            int arr[]=new int[n];
            int brr[]=new int[n];
            Pair<Integer, Integer> p[]=new Pair[n];
            for(i=0;i<n;i++){
                arr[i]=in.nextInt();
            }
            for(i=0;i<n;i++){
                brr[i]=in.nextInt();
                p[i]=new Pair<>(arr[i],brr[i]);
            }
            Arrays.sort(p);
            
            long ans=0;
            int curr=1,curc=1;
            for(i=0;i<n;i++){
                int nextr=p[i].x;
                int nextc=p[i].y;
                ans+=calcdist(curr,curc,nextr,nextc);
                curr=nextr;
                curc=nextc;
            }
            w.println(ans);
        }
        w.close();
    }
}