Guy-Manuel and Thomas are going to build a polygon spaceship.

You're given a strictly convex (i. e. no three points are collinear) polygon P which is defined by coordinates of its vertices. Define P(x,y) as a polygon obtained by translating P by vector \overrightarrow {(x,y)}. The picture below depicts an example of the translation:

<image>

Define T as a set of points which is the union of all P(x,y) such that the origin (0,0) lies in P(x,y) (both strictly inside and on the boundary). There is also an equivalent definition: a point (x,y) lies in T only if there are two points A,B in P such that \overrightarrow {AB} = \overrightarrow {(x,y)}. One can prove T is a polygon too. For example, if P is a regular triangle then T is a regular hexagon. At the picture below P is drawn in black and some P(x,y) which contain the origin are drawn in colored: 

<image>

The spaceship has the best aerodynamic performance if P and T are similar. Your task is to check whether the polygons P and T are [similar](https://tinyurl.com/vp5m7vl).

Input

The first line of input will contain a single integer n (3 ≤ n ≤ 10^5) — the number of points.

The i-th of the next n lines contains two integers x_i, y_i (|x_i|, |y_i| ≤ 10^9), denoting the coordinates of the i-th vertex.

It is guaranteed that these points are listed in counterclockwise order and these points form a strictly convex polygon.

Output

Output "YES" in a separate line, if P and T are similar. Otherwise, output "NO" in a separate line. You can print each letter in any case (upper or lower).

Examples

Input


4
1 0
4 1
3 4
0 3


Output


YES

Input


3
100 86
50 0
150 0


Output


nO

Input


8
0 0
1 0
2 1
3 3
4 6
3 6
2 5
1 3


Output


YES

Note

The following image shows the first sample: both P and T are squares. The second sample was shown in the statements.

<image>
import java.io.*;
import java.math.*;
import java.util.*;

/**
 *
 * @author Saju
 *
 */

public class Main {

	private static int dx[] = { -2, -3, -2, -1, -1, 1};
	private static int dy[] = { 1, -1, -1, -2, -3, -2};

	private static final long INF = (long) (1e15);
	private static final int INT_INF = Integer.MAX_VALUE;
	private static final long NEG_INF = Long.MIN_VALUE;
	private static final double EPSILON = 1e-10;

	private static final int MAX = 1007;
	private static final long MOD = 1000000007;
	
	private static final int MAXN = 100007;
	private static final int MAXA = 10000009;
	private static final int MAXLOG = 22;

	public static void main(String[] args) {

		InputReader in = new InputReader(System.in);
		PrintWriter out = new PrintWriter(System.out);
		

/*



*/
		
		int n = in.nextInt();
		Point[] points = new Point[n];
		for(int i = 0; i < n; i++) {
			long x = in.nextLong();
			long y = in.nextLong();
			
			points[i] = new Point(x, y);
		}
		
		if(n % 2 != 0) {
			System.out.println("NO");
		}
		else {
			boolean isOk = true;
			for(int i = 1; i <= n / 2; i++) {
				
				// line 1 -> i, i + 1
				int j = i;
				int k = i + 1;
				j--;
				k--;
				
				double line1Length = distance(points[j], points[k]);
				long slop1Up = points[j].y - points[k].y;
				long slop1Down = points[j].x - points[k].x;
				long gcd = gcd(slop1Up, slop1Down);
				slop1Up = slop1Up / gcd;
				slop1Down = slop1Down / gcd;
				
				// line 2 -> n / 2 + i, n / 2 + i + 1
				j = n / 2 + i;
				k = j + 1;
				j--;
				k--;
				if(k == n) {
					k = 0;
				}
				
				double line2Length = distance(points[j], points[k]);
				if(line1Length != line2Length) {
					isOk = false;
					break;
				}
				
				long slop2Up = points[j].y - points[k].y;
				long slop2Down = points[j].x - points[k].x;
				gcd = gcd(slop2Up, slop2Down);
				slop2Up = slop2Up / gcd;
				slop2Down = slop2Down / gcd;
				if(slop1Up != slop2Up || slop1Down != slop2Down) {
					isOk = false;
					break;
				}
				
			}
			if(isOk) {
				System.out.println("YES");
				
			}
			else {
				System.out.println("NO");
			}
		}
		
		out.flush();
		out.close();
		System.exit(0);
	}
	
	private static double distance(Point p1, Point p2) {
		long divx = p2.x - p1.x;
		long divy = p2.y - p1.y;
		divx = divx * divx;
		divy = divy * divy;
		return Math.sqrt(divx + divy);
	}
	
	private static String getBinaryStr(int n, int j) {
		String str = Integer.toBinaryString(n);
		int k = str.length();
		for(int i = 1; i <= j - k; i++) {
			str = "0" + str;
		}
		
		return str;
	}

	// O(log(max(A,M)))
	static long modInverse(long a, long m) {
		extendedEuclid(a, m);
		return (x % m + m) % m;
	}

	static long x;
	static long y;
	static long gcdx;

	private static void extendedEuclid(long a, long b) {
		if (b == 0) {
			gcdx = a;
			x = 1;
			y = 0;
		} else {
			extendedEuclid(b, a % b);
			long temp = x;
			x = y;
			y = temp - ((a / b) * y);
		}
	}
	
	private static void generatePrime(int n) {
		 //O(NloglogN)
		boolean arr[] = new boolean[n + 5];
		Arrays.fill(arr, true);
		for(int i = 2; i * i <=n; i++){
			if(arr[i] == true){
				for(int j = i * i; j <= n; j+=i){
					arr[j] = false; 
				}
			}
		}
		int count = 0;
		int start = 0;
		for(int i = 2; i <= n; i++){
			if(arr[i] == true){
//				System.out.println(i + " ");
				count++;
			}
			if(count == (start * 100) + 1) {
//				System.out.println(i);
				start++;
			}
		}
		System.out.println();
		System.out.println(count);
		
	}
	
	private static Map<Long, Long> primeFactorization(long n, long m){
		Map<Long, Long> map = new HashMap<>();
		
		for(long i = 2; i <= Math.sqrt(n); i++){
			if(n % i == 0){
			long count = 0;
			while(n % i == 0){
				count++;
				n = n / i;
			}
			long val = count * m;
			map.put(i, val);
//			System.out.println("i: " + i + ", count: " + count);
		}
			
		}
		if(n != 1) {
//			System.out.println(n);
			map.put(n, m);
		}
		return map;
	}

	private static class Pair<T>{
		T a;
		T b;
		Pair(T a, T b){
			this.a = a;
			this.b = b;
		}
	}
	
	private static class SegmentTree{
		int n;
		private final int MAXN = 100007;
		private long[] tree = new long[MAXN << 2];
		private long[] lazy = new long[MAXN << 2];
		private long[] arr = new long[MAXN];
		
		
		/***
		 * 
		 * arr is 1 based index.
		 * 
		 * @param arr
		 * 
		 */
		SegmentTree(int n, long[] arr){
			this.n = n;
			for(int i = 0; i < arr.length; i++) {
				this.arr[i] = arr[i];
			}
		}
		
		void build(int index, int left, int right) {
			if(left == right) {
				tree[index] = arr[left];
			}
			else {
				int mid = (left + right) / 2;
				
				build(index * 2, left, mid);
				build((index * 2) + 1, mid + 1, right);
				tree[index] = max(tree[(index * 2)], tree[(index * 2) + 1]);
			}
		}
		
		long query(int node, int left, int right, int start, int end) {
			
			if(left > end || right < start) {
				return NEG_INF;
			}
			
			if(left >= start && right <= end) {
				return tree[node];
			}
			int mid = (left + right) / 2;
			long val1 = query(2 * node, left, mid, start, end);
			long val2 = query(2 * node + 1, mid + 1, right, start, end);
			
			return max(val1, val2);
		}
		
		void update(int node, int left, int right, int idx, long val) {
			if(left == right) {
				tree[node] += val;
			}
			else {
				int mid = (left + right) / 2;
				if(idx <= mid) {
					update(2 * node, left, mid, idx, val);
				}
				else {
					update(2 * node + 1, mid + 1, right, idx, val);
				}
				tree[node] = max(tree[(2 * node) + 1], tree[(2 * node)]);
			}
		}
		
		

		 void updateRange(int node, int start, int end, int l, int r, long val)
		{
		    if(lazy[node] != 0)
		    { 
		        // This node needs to be updated
		        tree[node] =  lazy[node];    // Update it
		        if(start != end)
		        {
		            lazy[node*2] = lazy[node];                  // Mark child as lazy
		            lazy[node*2+1] = lazy[node];                // Mark child as lazy
		        }
		        lazy[node] = 0;                                  // Reset it
		    }
		    if(start > end || start > r || end < l)              // Current segment is not within range [l, r]
		        return;
		    if(start >= l && end <= r)
		    {
		        // Segment is fully within range
		        tree[node] =  val;
		        if(start != end)
		        {
		            // Not leaf node
		            lazy[node*2] = val;
		            lazy[node*2+1] = val;
		        }
		        return;
		    }
		    int mid = (start + end) / 2;
		    updateRange(node*2, start, mid, l, r, val);        // Updating left child
		    updateRange(node*2 + 1, mid + 1, end, l, r, val);   // Updating right child
		    tree[node] = max(tree[node*2], tree[node*2+1]);        // Updating root with max value 
		}

		 long queryRange(int node, int start, int end, int l, int r)
		{
		    if(start > end || start > r || end < l)
		        return 0;         // Out of range
		    if(lazy[node] != 0)
		    {
		        // This node needs to be updated
		        tree[node] =  lazy[node];            // Update it
		        if(start != end)
		        {
		            lazy[node*2] = lazy[node];         // Mark child as lazy
		            lazy[node*2+1] = lazy[node];    // Mark child as lazy
		        }
		        lazy[node] = 0;                 // Reset it
		    }
		    if(start >= l && end <= r)             // Current segment is totally within range [l, r]
		        return tree[node];
		    int mid = (start + end) / 2;
		    long p1 = queryRange(node*2, start, mid, l, r);         // Query left child
		    long p2 = queryRange(node*2 + 1, mid + 1, end, l, r); // Query right child
		    return max(p1, p2);
		}
		
		 void buildRange(int node, int low, int high){
			if(low == high){
				tree[node] =  arr[low];
				return;
			}
			
			int mid = (low + high) / 2;
			int left = node << 1;
			int right = left | 1;
			buildRange(left, low, mid);
			buildRange(right, mid + 1, high);
			tree[node] = max(tree[left], tree[right]);
		}
		
		
		void printSegmentTree() {
			System.out.println(Arrays.toString(tree));
		}
		
	}
	
	private static class KMP{
		
		private static char[] t;
		private static char[] s;
		
		public int kmp(char[]t, char[]s) {
			this.t = t;
			this.s = s;
			return this.kmp();
		}
		
		private int kmp() {
			
			List<Integer> prefixTable = getPrefixTable(s);
			
			int match = 0;
			int i = 0;
			int j = 0;
			
			int n = t.length;
			int m = s.length;
			while(i < n) {
				if(t[i] == s[j]) {
					if(j == m - 1) {
						match++;
						j = prefixTable.get(j - 1);
						continue;
					}
					i++;
					j++;
				}
				else if(j > 0) {
					j = prefixTable.get(j - 1);
				}
				else {
					i++;
				}
			}
			
			return match;
		}

		/***
		1. We compute the prefix values π[i] in a loop by iterating 	<br/>
				from i=1 to i=n−1 (π[0] just gets assigned with 0).		<br/><br/>
		2. To calculate the current value π[i] we set the variable j 	<br/>
				denoting the length of the best suffix for i−1. Initially j=π[i−1].	<br/>
		3. Test if the suffix of length j+1 is also a prefix by		 <br/><br/>
				comparing s[j] and s[i]. If they are equal then we assign π[i]=j+1, 	<br/>
				otherwise we reduce j to π[j−1] and repeat this step.		<br/><br/>
		4. If we have reached the length j=0 and still don't have a match,	<br/> 
				then we assign π[i]=0 and go to the next index i+1.		<br/><br/>
				
		@param
	 	pattern(String)
	***/
		private List<Integer> getPrefixTable(char[] pattern){
			
			List<Integer> prefixTable = new ArrayList<Integer>();
			int n = pattern.length;
			for(int i = 0; i < n; i++) {
				prefixTable.add(0);
			}
			
			for(int i = 1; i < n; i++) {
				for(int j = prefixTable.get(i - 1); j >= 0;) {
					if(pattern[j] == pattern[i]) {
						prefixTable.set(i, j + 1);
						break;
					}
					else if(j > 0){
						j = prefixTable.get(j - 1);
					}
					else {
						break;
					}
				}
			}
			
			return prefixTable;
		}
	}
	


	private static class Point {
		long x;
		long y;
		Point(long x, long y){
			this.x = x;
			this.y = y;
		}
		
		@Override
		public boolean equals(Object obj) {
			Point ob = (Point) obj;
			if(this.x == ob.x && this.y == ob.y){
				return true;
			}
			return false;
			
		}
		@Override
		public String toString() {
			return this.x + " " + this.y;
		}
		
		@Override
		public int hashCode() {
		    return 0;
		}
	}

	private static long pow(int base, int pow) {
		long val = 1L;
		for(int i = 1; i <= pow; i++) {
			val *= base;
		}
		return val;
	}
	
	private static int log(int x, int base) {
		return (int) (Math.log(x) / Math.log(base));
	}
	private static int log(long x, int base) {
		return (int) (Math.log(x) / Math.log(base));
	}
	private static long max(long a, long b) {
		if (a >= b) {
			return a;
		}
		return b;
	}

	private static long abs(long a) {
		if (a < 0) {
			return -a;
		}
		return a;
	}

	private static int abs(int a) {
		if (a < 0) {
			return -a;
		}
		return a;
	}

	private static int max(int a, int b) {
		if (a >= b) {
			return a;
		}
		return b;
	}

	private static int min(int a, int b) {
		if (a <= b) {
			return a;
		}
		return b;
	}
	
	private static long min(long a, long b) {
		if (a <= b) {
			return a;
		}
		return b;
	}

	private static long gcd(long a, long b) {
		if (b == 0) {
			return a;
		}
		return gcd(b, a % b);
	}

	private static int gcd(int a, int b) {
		if (b == 0) {
			return a;
		}
		return gcd(b, a % b);
	}

	private static long bigMod(long n, long k, long m) {

		long ans = 1;
		while (k > 0) {
			if ((k & 1) == 1) {
				ans = (ans * n) % m;
			}
			n = (n * n) % m;
			k >>= 1;
		}
		return ans;
	}

	/*
	 * Returns an iterator pointing to the first element in the range [first,
	 * last] which does not compare less than val.
	 * 
	 */
	private static int lowerBoundNew(long[] arr, long num) {
		int start = 0;
		int end = arr.length - 1;
		int index = 0;
		int len = arr.length;
		int mid = 0;
		while (true) {
			if (start > end) {
				break;
			}
			mid = (start + end) / 2;
			if (arr[mid] > num) {
				end = mid - 1;
			} else if (arr[mid] < num) {
				start = mid + 1;
			} else {
				while (mid >= 0 && arr[mid] == num) {
					mid--;
				}
				return mid + 1;
			}
		}
		if (arr[mid] < num) {
			return mid + 1;
		}
		return mid;
	}

	/*
	 * upper_bound() is a standard library function in C++ defined in the header
	 * . It returns an iterator pointing to the first element in the range
	 * [first, last) that is greater than value, or last if no such element is
	 * found
	 * 
	 */
	private static int upperBoundNew(long[] arr, long num) {

		int start = 0;
		int end = arr.length - 1;
		int index = 0;
		int len = arr.length;
		int mid = 0;
		while (true) {
			if (start > end) {
				break;
			}
			mid = (start + end) / 2;
			if (arr[mid] > num) {
				end = mid - 1;
			} else if (arr[mid] < num) {
				start = mid + 1;
			} else {
				while (mid < len && arr[mid] == num) {
					mid++;
				}
				if (mid == len - 1 && arr[mid] == num) {
					return mid + 1;
				} else {
					return mid;
				}
			}
		}
		if (arr[mid] < num) {
			return mid + 1;
		}
		return mid;
	}

	private static class InputReader {
		public BufferedReader reader;
		public StringTokenizer tokenizer;

		public InputReader(InputStream stream) {
			reader = new BufferedReader(new InputStreamReader(stream));
			tokenizer = null;
		}

		public String next() {
			try {
				while (tokenizer == null || !tokenizer.hasMoreTokens()) {
					tokenizer = new StringTokenizer(reader.readLine());

				}
			} catch (IOException e) {
				return null;
			}
			return tokenizer.nextToken();
		}

		public String nextLine() {
			String line = null;
			try {
				tokenizer = null;
				line = reader.readLine();
			} catch (IOException e) {
				throw new RuntimeException(e);
			}
			return line;
		}

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

		public double nextDouble() {
			return Double.parseDouble(next());
		}

		public long nextLong() {
			return Long.parseLong(next());
		}

		public boolean hasNext() {
			try {
				while (tokenizer == null || !tokenizer.hasMoreTokens()) {
					tokenizer = new StringTokenizer(reader.readLine());
				}
			} catch (Exception e) {
				return false;
			}
			return true;
		}
	}
}