1551_D1. Domino (easy version)_43
The only difference between this problem and D2 is that you don't have to provide the way to construct the answer in this problem, but you have to do it in D2.

There's a table of n × m cells (n rows and m columns). The value of n ⋅ m is even.

A domino is a figure that consists of two cells having a common side. It may be horizontal (one of the cells is to the right of the other) or vertical (one of the cells is above the other).

You need to find out whether it is possible to place nm/2 dominoes on the table so that exactly k of them are horizontal and all the other dominoes are vertical. The dominoes cannot overlap and must fill the whole table.

Input

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

Each test case consists of a single line. The line contains three integers n, m, k (1 ≤ n,m ≤ 100, 0 ≤ k ≤ nm/2, n ⋅ m is even) — the number of rows, columns and horizontal dominoes, respectively.

Output

For each test case output "YES", if it is possible to place dominoes in the desired way, or "NO" otherwise.

You may print each letter in any case (YES, yes, Yes will all be recognized as positive answer, NO, no and nO will all be recognized as negative answer).

Example

Input


8
4 4 2
2 3 0
3 2 3
1 2 0
2 4 2
5 2 2
2 17 16
2 1 1


Output


YES
YES
YES
NO
YES
NO
YES
NO
import java.io.BufferedReader;
    import java.io.IOException;
    import java.io.InputStreamReader;
    import java.io.PrintWriter;
import java.lang.reflect.Array;
import java.util.*;
public class Main{
    static class FastScanner {
            BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
            StringTokenizer st = new StringTokenizer("");

            String next() {
                while (!st.hasMoreTokens())
                    try {
                        st = new StringTokenizer(br.readLine());
                    } catch (IOException e) {
                        e.printStackTrace();
                    }
                return st.nextToken();
            }

            int nextInt() {
                return Integer.parseInt(next());
            }

            int[] nextArray(int n) {
                int[] a = new int[n];
                for (int i = 0; i < n; i++) a[i] = nextInt();
                return a;
            }
            long[] nextArray(long n) {
                long[] a = new long[(int) n];
                for (int i = 0; i < n; i++) a[i] = nextLong();
                return a;
            }

            long nextLong() {
                return Long.parseLong(next());
            }
        }
    static class FastWriter extends PrintWriter {
            FastWriter(){
                super(System.out);
            }
            void println(int[] array) {
                for(int i=0; i<array.length; i++) {
                    print(array[i]+" ");
                }
                println();
            }
            void println(long [] array) {
                for(int i=0; i<array.length; i++) {
                    print(array[i]+" ");
                }
                println();
            }
        }
    static int MOD=1000003;
    public static void main(String[] args) throws IOException {
        FastScanner in = new FastScanner();
        FastWriter out = new FastWriter();
        int t=in.nextInt();
        //int t=1;
        while (t-->0){
            int n=in.nextInt();
            int m=in.nextInt();
            int k=in.nextInt();
            int max=(n*m)/2;
            if(n%2!=0){
                if(k<m/2){
                    out.println("NO");
                }else {
                    k-=m/2;
                    if(k%2!=0){
                        out.println("NO");
                    }else {
                        out.println("YES");
                    }
                }
            }else if(m%2!=0){
                int hh=max-n/2;
                if(k>hh){
                    out.println("NO");
                }else {
                    if(k%2!=0){
                        out.println("NO");
                    }else {
                        out.println("YES");
                    }
                }
            }else {
                if(k%2!=0){
                    out.println("NO");
                }else {
                    out.println("YES");
                }
            }
        }
        out.close();
    }
    //Arrays.sort(a, (o1, o2) -> (o1[0] - o2[0]));
    static int totalPrimeFactors(int n) {
        int cnt=0;
        while (n%2==0) {
            cnt++;
            n /= 2;
        }
        int num= (int) Math.sqrt(n);
        for (int i = 3; i <= num; i+= 2) {
            while (n%i == 0) {
                cnt++;
                n /= i;
                num=(int)Math.sqrt(n);
            }
        }
        if (n > 2){
            cnt++;
        }
        return cnt;
    }
    static char get(int i){
        return (char)(i+'a');
    }
    static boolean distinct(int num){
        HashSet<Integer> set=new HashSet<>();
        int len=String.valueOf(num).length();
        while (num!=0){
            set.add(num%10);
            num/=10;
        }
        return set.size()==len;
    }
    static int maxSubArraySum(int a[],int st,int en) {
        int max_s = Integer.MIN_VALUE, max_e = 0,ind=0,ind1=1;
        for (int i = st; i <= en; i++) {
            max_e+= a[i];
            if (max_s < max_e){
                max_s = max_e;
                ind=ind1;
            }
            if (max_e < 0){
                max_e = 0;
                ind1=i+1;
            }
        }
        if(st==0){
            return max_s;
        }
        if(ind==1){
            return a[0]+2*max_s;
        }else {
            return 2*max_s+maxSubArraySum(a,0,ind-1);
        }
        //return max_s;
    }
    static void segmentedSieve(ArrayList<Integer> res,int low, int high) {
        if(low < 2){
            low = 2;
        }
        ArrayList<Integer> prime = new ArrayList<>();
        sS2(high, prime);
        boolean[] mark = new boolean[high - low + 1];
        Arrays.fill(mark, true);
        for (int i = 0; i < prime.size(); i++) {
            int loLim = (low / prime.get(i)) * prime.get(i);
            if (loLim < low){
                loLim += prime.get(i);
            }
            if (loLim == prime.get(i)){
                loLim += prime.get(i);
            }
            for (int j = loLim; j <= high; j += prime.get(i)) {
                mark[j - low] = false;
            }
        }
        for (int i = low; i <= high; i++) {
            if (mark[i - low]){
                System.out.println(i);
                res.add(i);
            }
        }
    }
    static void sS2(int limit, ArrayList<Integer> prime) {
        int bound = (int)Math.sqrt(limit);
        boolean[] mark = new boolean[bound + 1];
        for (int i = 0; i <= bound; i++){
            mark[i] = true;
        }
        for (int i = 2; i * i <= bound; i++) {
            if (mark[i]) {
                for (int j = i * i; j <= bound; j += i){
                    mark[j] = false;
                }
            }
        }
        for (int i = 2; i <= bound; i++) {
            if (mark[i]){
                prime.add(i);
            }
        }
    }
    static boolean[] sieveOfEratosthenes(int n){
        boolean[] prime = new boolean[n + 1];
        Arrays.fill(prime,true);
        prime[0]=false;prime[1]=false;
        for (int p = 2; p * p <= n; p++) {
            if(prime[p]){
                for (int i = p * p; i <= n; i += p){
                    prime[i] = false;
                }
            }
        }
        return prime;
    }
    static int highestPowerOf2(int n) {
        if (n < 1){ return 0; }
        int res = 1;
        for (int i = 0; i < 8 * Integer.BYTES; i++) {
            int curr = 1 << i;
            if (curr > n){ break; }
            res = curr;
        }
        return res;
    }
    static int reduceFraction(int x, int y) {
        int d= gcd(x, y);
        return x/d+y/d;
    }
    static boolean subset(int[] ar,int n,int sum){
        if(sum==0){
            return true;
        }
        if(n<0||sum<0){
            return false;
        }
        return subset(ar,n-1,sum)||subset(ar,n-1,sum-ar[n]);
    }
    static boolean isPrime(int n){
        if(n<=1) return false;
        for(int i = 2;i<=Math.sqrt(n);i++){
            if (n % i == 0) return false;
        }
        return true;
    }
    static int gcd(int a, int b) {
        if (b == 0) return a;
        return gcd(b, a % b);
    }
    static long gcd(long a, long b) {
        if (b == 0) return a;
        return gcd(b, a % b);
    }
    static long lcm(long a, long b) {
        return (a * b) / gcd(a, b);
    }
    static int lcm(int a, int b) {
        return (a * b) / gcd(a, b);
    }
    static boolean isPowerOfTwo(long n) {
        if(n==0){
            return false;
        }
        while (n%2==0){
            n/=2;
        }
        return n==1;
    }
    static boolean isPerfectSquare(int x){
        if (x >= 0) {
            int sr = (int)Math.sqrt(x);
            return ((sr * sr) == x);
        }
        return false;
    }
    static int lower_bound(int[] arr, int x) {
        int low_limit = 0, high_limit = arr.length, mid;
        while (low_limit < high_limit) {
            mid = (low_limit + high_limit) / 2;
            if (arr[mid] >= x){
                high_limit = mid;
            }else{
                low_limit = mid + 1;
            }
        }
        return low_limit;
    }
    static int upper_bound(int[] arr, int x) {
        int low_limit = 0, high_limit = arr.length, mid;
        while (low_limit < high_limit) {
            mid = (low_limit + high_limit) / 2;
            if (arr[mid] > x){
                high_limit = mid;
            }else{
                low_limit = mid + 1;
            }
        }
        return low_limit;
    }
    static int binarySearch(int[] ar,int n,int num){
        int low=0,high=n-1;
        while (low<=high){
            int mid=(low+high)/2;
            if(ar[mid]==num){
                return mid;
            }else if(ar[mid]>num){
                high=mid-1;
            }else {
                low=mid+1;
            }
        }
        return -1;
    }
    static int fib(int n) {
        long[][] F = new long[][]{{1,1},{1,0}};
        if (n == 0){
            return 0;
        }
        power(F, n-1);
        return (int)F[0][0];
    }
    static void multiply(long F[][], long M[][]) {
        long x =  (F[0][0]*M[0][0])%1000000007 + (F[0][1]*M[1][0])%1000000007;
        long y =  (F[0][0]*M[0][1])%1000000007 + (F[0][1]*M[1][1])%1000000007;
        long z =  (F[1][0]*M[0][0])%1000000007 + (F[1][1]*M[1][0])%1000000007;
        long w =  (F[1][0]*M[0][1])%1000000007 + (F[1][1]*M[1][1])%1000000007;
        F[0][0] = x%1000000007;
        F[0][1] = y%1000000007;
        F[1][0] = z%1000000007;
        F[1][1] = w%1000000007;
    }
    static void power(long F[][], int n) {
        if( n == 0 || n == 1){
            return;
        }
        long M[][] = new long[][]{{1,1},{1,0}};
        power(F, n/2);
        multiply(F, F);
        if (n%2 != 0){
            multiply(F, M);
        }
    }
    static int binaryExponentiation(int x,int n){
        int ans=1;
        while (n>0){
            if(n%2!=0){
                ans=(ans*x)%MOD;
            }
            x=(x*x)%MOD;
            n/=2;
        }
        return ans;
    }
    static void bfs(ArrayList<Integer>[] ar,int node){
        boolean[] visited=new boolean[ar.length];
        Queue<Integer> queue=new LinkedList<>();
        visited[node]=true;
        queue.add(node);
        while(!queue.isEmpty()){
            int nn=queue.poll();
            System.out.print(nn+" ");
            for(int n : ar[nn]) {
                if (!visited[n]) {
                    visited[n] = true;
                    queue.add(n);
                }
            }
        }
        System.out.println();
    }
    static void dfs(ArrayList<Integer>[] ar,int node){
        boolean[] visited=new boolean[ar.length];
        dfsUtil(ar,node,visited);
        System.out.println();
    }
    static void dfsUtil(ArrayList<Integer>[] ar,int node,boolean[] visited){
        visited[node]=true;
        //System.out.print(node+" ");
        for(Integer n:ar[node]){
            if(!visited[n]){
                dfsUtil(ar,n,visited);
            }
        }
    }
}