Problem:
Score : 300 points

Problem Statement

Snuke has N hats. The i-th hat has an integer a_i written on it.

There are N camels standing in a circle.
Snuke will put one of his hats on each of these camels.

If there exists a way to distribute the hats to the camels such that the following condition is satisfied for every camel, print Yes; otherwise, print No.

The bitwise XOR of the numbers written on the hats on both adjacent camels is equal to the number on the hat on itself.

What is XOR?

The bitwise XOR x_1 \oplus x_2 \oplus \ldots \oplus x_n of n non-negative integers x_1, x_2, \ldots, x_n is defined as follows:

- When x_1 \oplus x_2 \oplus \ldots \oplus x_n is written in base two, the digit in the 2^k's place (k \geq 0) is 1 if the number of integers among x_1, x_2, \ldots, x_n whose binary representations have 1 in the 2^k's place is odd, and 0 if that count is even.

For example, 3 \oplus 5 = 6.

Constraints

All values in input are integers.

3 \leq N \leq 10^{5}

0 \leq a_i \leq 10^{9}

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 \ldots a_{N}

Output

Print the answer.

Sample Input 1

3
1 2 3

Sample Output 1

Yes

If we put the hats with 1, 2, and 3 in this order, clockwise, the condition will be satisfied for every camel, so the answer is Yes.

Sample Input 2

4
1 2 4 8

Sample Output 2

No

There is no such way to distribute the hats; the answer is No.

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)



import java.io.*;
import java.util.*;

public class Main {
    static StringBuilder sb = new StringBuilder();
    static FastScanner sc = new FastScanner(System.in);
    static int INF = 12345678;
    static long MOD = 1000000007;
    static int[] y4 = {0, 1, 0, -1};
    static int[] x4 = {1, 0, -1, 0};
    static int[] y8 = {0, 1, 0, -1, -1, 1, 1, -1};
    static int[] x8 = {1, 0, -1, 0, 1, -1, 1, -1};
    static long[] F;//factorial
    static boolean[] isPrime;
    static int[] primes;
    static char[][] map;

    static int N, M;
    static long T;
    static int[] A;


    public static void main(String[] args) {

        int n = sc.nextInt();

        List<Long> list = new ArrayList<>();
        HashMap<Long,Integer> map = new HashMap<>();

        if(n % 3 != 0){
            System.out.println("No");
            return;
        }

        for (int i = 0; i < n; i++) {
            long temp = sc.nextLong();
            map.merge(temp,1,Integer::sum);
            if(!list.contains(temp)){
                list.add(temp);
//                System.out.println(temp);
            }
        }

        if(list.size()!=3){
            System.out.println("No");
            return;
        }

        if(map.get(list.get(0)) == map.get(list.get(1)) && map.get(list.get(1)) == map.get(list.get(2))){
            if((list.get(0) ^ list.get(1)) == list.get(2)){
//                System.out.printf("%d %d %d",map.get(list.get(0)),map.get(list.get(1)),map.get(list.get(2)));
                System.out.println("Yes");
            }else{
//                System.out.printf("%d %d %d",map.get(list.get(0)),map.get(list.get(1)),map.get(list.get(2)));
                System.out.println("No");
            }
        }else{
            System.out.println("No");
        }


    }

    static class Dijkstra {
        long initValue = -1;
        Node[] nodes;
        int n;
        long[] d;

        Dijkstra(int n) {
            this.n = n;
            nodes = new Node[n];
            for (int i = 0; i < n; i++)
                nodes[i] = new Node(i);
            d = new long[n];
            Arrays.fill(d, initValue);
        }

        Dijkstra(int n, int edge, boolean isDirectedGraph) {
            this.n = n;

            nodes = new Node[n];
            for (int i = 0; i < n; i++)
                nodes[i] = new Node(i);

            d = new long[n];
            Arrays.fill(d, initValue);
            if (isDirectedGraph) {
                for (int ei = 0; ei < edge; ei++) {
                    int f = sc.nextInt() - 1;
                    int t = sc.nextInt() - 1;
                    long c = sc.nextLong();
                    addEdge(f, t, c);
                }
            } else {
                for (int ei = 0; ei < edge; ei++) {
                    int f = sc.nextInt() - 1;
                    int t = sc.nextInt() - 1;
                    long c = sc.nextLong();
                    addEdge(f, t, c);
                    addEdge(t, f, c);
                }
            }
        }

        void addEdge(int f, int t, long c) {
            nodes[f].edges.add(new Edge(t, c));
        }

        long[] solve(int s) {
            d[s] = 0;
            //最短距離と頂点を持つ
            PriorityQueue<Dis> q = new PriorityQueue<>();
            q.add(new Dis(s, 0));
            while (!q.isEmpty()) {
                Dis now = q.poll();
                int nowId = now.p;
                long nowC = now.cos;
                for (Edge edge : nodes[nowId].edges) {
                    int to = edge.toId;
                    long needsCost = edge.toCost + nowC;
                    if (d[to] == initValue || needsCost < d[to]) {
                        d[to] = needsCost;
                        q.add(new Dis(to, needsCost));
                    }
                }
            }
            return d;
        }

        //O( E ^ 2) 辺が密の時用
        long[] solve2(int s) {
            boolean[] used = new boolean[n];
            long[][] cost = new long[n][n];
            Main.fill(cost, initValue);
            Arrays.fill(d, initValue);
            d[s] = 0;

            for (Node node : nodes) {
                for (Edge edge : node.edges) {
                    int fromId = node.id;
                    int toId = edge.toId;
                    long toCost = edge.toCost;
                    cost[fromId][toId] = toCost;
                }
            }
            while (true) {
                int v = -1;
                //まだ使われていない頂点のうち、距離が最小のものを探す。
                for (int u = 0; u < n; u++)
                    if (!used[u] && (v == -1 || d[u] < d[v])) v = u;
                if (v == -1) break;
                used[v] = true;
                for (int u = 0; u < n; u++)
                    d[u] = Math.min(d[u], d[v] + cost[v][u]);
            }
            return d;
        }

        static class Dis implements Comparable<Dis> {
            //現在地点 最短距離
            int p;
            long cos;

            Dis(int p, long cost) {
                this.p = p;
                cos = cost;
            }

            public int compareTo(Dis d) {
                if (cos != d.cos) {
                    if (cos > d.cos) return 1;
                    else if (cos == d.cos) return 0;
                    else return -1;
                } else {
                    return p - d.p;
                }
            }
        }

        static class Node {
            int id;
            List<Edge> edges;

            Node(int id) {
                edges = new ArrayList<>();
                this.id = id;
            }
        }

        static class Edge {
            int toId;
            long toCost;

            Edge(int id, long cost) {
                toId = id;
                toCost = cost;
            }

        }
    }

    public static long toLong(int[] ar) {
        long res = 0;
        for (int i : ar) {
            res *= 10;
            res += i;
        }
        return res;
    }

    public static int toInt(int[] ar) {
        int res = 0;
        for (int i : ar) {
            res *= 10;
            res += i;
        }
        return res;
    }

    //k個の次の組み合わせをビットで返す 大きさに上限はない 110110 -> 111001
    public static int nextCombSizeK(int comb, int k) {
        int x = comb & -comb; //最下位の1
        int y = comb + x; //連続した下の1を繰り上がらせる
        return ((comb & ~y) / x >> 1) | y;
    }

    public static int keta(long num) {
        int res = 0;
        while (num > 0) {
            num /= 10;
            res++;
        }
        return res;
    }

    public static long getHashKey(int a, int b) {
        return (long) a << 32 | b;
    }

    public static boolean isOutofIndex(int x, int y) {
        if (x < 0 || y < 0) return true;
        if (map[0].length <= x || map.length <= y) return true;
        return false;
    }

    public static void setPrimes() {
        int n = 100001;
        isPrime = new boolean[n];
        List<Integer> prs = new ArrayList<>();
        Arrays.fill(isPrime, true);
        isPrime[0] = isPrime[1] = false;
        for (int i = 2; i * i <= n; i++) {
            if (!isPrime[i]) continue;
            prs.add(i);
            for (int j = i * 2; j < n; j += i) {
                isPrime[j] = false;
            }
        }
        primes = new int[prs.size()];
        for (int i = 0; i < prs.size(); i++)
            primes[i] = prs.get(i);
    }

    public static void revSort(int[] a) {
        Arrays.sort(a);
        reverse(a);
    }

    public static void revSort(long[] a) {
        Arrays.sort(a);
        reverse(a);
    }

    public static int[][] copy(int[][] ar) {
        int[][] nr = new int[ar.length][ar[0].length];
        for (int i = 0; i < ar.length; i++)
            for (int j = 0; j < ar[0].length; j++)
                nr[i][j] = ar[i][j];
        return nr;
    }

    /**
     * <h1>指定した値以上の先頭のインデクスを返す</h1>
     * <p>配列要素が０のときは、０が返る。</p>
     *
     * @return<b>int</b> ： 探索した値以上で、先頭になるインデクス
     * 値が無ければ、挿入できる最小のインデックス
     */
    public static int lowerBound(final int[] arr, final int value) {
        int low = 0;
        int high = arr.length;
        int mid;

        while (low < high) {
            mid = ((high - low) >>> 1) + low;    //(low + high) / 2 (オーバーフロー対策)
            if (arr[mid] < value) {
                low = mid + 1;
            } else {
                high = mid;
            }
        }
        return low;
    }

    /**
     * <h1>指定した値より大きい先頭のインデクスを返す</h1>
     * <p>配列要素が０のときは、０が返る。</p>
     *
     * @return<b>int</b> ： 探索した値より上で、先頭になるインデクス
     * 値が無ければ、挿入できる最小のインデックス
     */
    public static int upperBound(final int[] arr, final int value) {
        int low = 0;
        int high = arr.length;
        int mid;
        while (low < high) {
            mid = ((high - low) >>> 1) + low;    //(low + high) / 2 (オーバーフロー対策)
            if (arr[mid] <= value) {
                low = mid + 1;
            } else {
                high = mid;
            }
        }
        return low;
    }

    /**
     * <h1>指定した値以上の先頭のインデクスを返す</h1>
     * <p>配列要素が０のときは、０が返る。</p>
     *
     * @return<b>int</b> ： 探索した値以上で、先頭になるインデクス
     * 値がなければ挿入できる最小のインデックス
     */
    public static long lowerBound(final long[] arr, final long value) {
        int low = 0;
        int high = arr.length;
        int mid;
        while (low < high) {
            mid = ((high - low) >>> 1) + low;    //(low + high) / 2 (オーバーフロー対策)
            if (arr[mid] < value) {
                low = mid + 1;
            } else {
                high = mid;
            }
        }
        return low;
    }

    /**
     * <h1>指定した値より大きい先頭のインデクスを返す</h1>
     * <p>配列要素が０のときは、０が返る。</p>
     *
     * @return<b>int</b> ： 探索した値より上で、先頭になるインデクス
     * 値がなければ挿入できる最小のインデックス
     */
    public static long upperBound(final long[] arr, final long value) {
        int low = 0;
        int high = arr.length;
        int mid;
        while (low < high) {
            mid = ((high - low) >>> 1) + low;    //(low + high) / 2 (オーバーフロー対策)
            if (arr[mid] <= value) {
                low = mid + 1;
            } else {
                high = mid;
            }
        }
        return low;
    }

    //次の順列に書き換える、最大値ならfalseを返す
    public static boolean nextPermutation(int A[]) {
        int len = A.length;
        int pos = len - 2;
        for (; pos >= 0; pos--) {
            if (A[pos] < A[pos + 1]) break;
        }
        if (pos == -1) return false;

        //posより大きい最小の数を二分探索
        int ok = pos + 1;
        int ng = len;
        while (Math.abs(ng - ok) > 1) {
            int mid = (ok + ng) / 2;
            if (A[mid] > A[pos]) ok = mid;
            else ng = mid;

        }

        swap(A, pos, ok);
        reverse(A, pos + 1, len - 1);


        return true;
    }

    //次の順列に書き換える、最小値ならfalseを返す
    public static boolean prevPermutation(int A[]) {
        int len = A.length;
        int pos = len - 2;
        for (; pos >= 0; pos--) {
            if (A[pos] > A[pos + 1]) break;
        }
        if (pos == -1) return false;

        //posより小さい最大の数を二分探索
        int ok = pos + 1;
        int ng = len;
        while (Math.abs(ng - ok) > 1) {
            int mid = (ok + ng) / 2;
            if (A[mid] < A[pos]) ok = mid;
            else ng = mid;

        }

        swap(A, pos, ok);
        reverse(A, pos + 1, len - 1);


        return true;
    }

    //↓nCrをmod計算するために必要。　***factorial(N)を呼ぶ必要がある***
    static long ncr(int n, int r) {
        if (n < r) return 0;
        else if (r == 0) return 1;

        factorial(n);
        return F[n] / (F[n - r] * F[r]);
    }

    static long ncr2(int a, int b) {
        if (b == 0) return 1;
        else if (a < b) return 0;
        long res = 1;
        for (int i = 0; i < b; i++) {
            res *= a - i;
            res /= i + 1;
        }
        return res;
    }

    static long ncrdp(int n, int r) {
        if (n < r) return 0;
        long[][] dp = new long[n + 1][r + 1];
        for (int ni = 0; ni < n + 1; ni++) {
            dp[ni][0] = dp[ni][ni] = 1;
            for (int ri = 1; ri < ni; ri++) {
                dp[ni][ri] = dp[ni - 1][ri - 1] + dp[ni - 1][ri];
            }
        }
        return dp[n][r];
    }

    static long modNcr(int n, int r) {
        if (n < r) return 0;
        long result = F[n];
        result = result * modInv(F[n - r]) % MOD;
        result = result * modInv(F[r]) % MOD;
        return result;
    }

    public static long modSum(long... lar) {
        long res = 0;
        for (long l : lar)
            res = (res + l % MOD) % MOD;
        return res;
    }

    public static long modDiff(long a, long b) {
        long res = a - b;
        if (res < 0) res += MOD;
        res %= MOD;
        return res;
    }

    public static long modMul(long... lar) {
        long res = 1;
        for (long l : lar)
            res = (res * l) % MOD;
        if (res < 0) res += MOD;
        res %= MOD;
        return res;
    }

    public static long modDiv(long a, long b) {
        long x = a % MOD;
        long y = b % MOD;
        long res = (x * modInv(y)) % MOD;
        return res;
    }

    static long modInv(long n) {
        return modPow(n, MOD - 2);
    }

    static void factorial(int n) {
        F = new long[n + 1];
        F[0] = F[1] = 1;
//        for (int i = 2; i <= n; i++)
//        {
//            F[i] = (F[i - 1] * i) % MOD;
//        }
        //
        for (int i = 2; i <= 100000; i++) {
            F[i] = (F[i - 1] * i) % MOD;
        }
        for (int i = 100001; i <= n; i++) {
            F[i] = (F[i - 1] * i) % MOD;
        }
    }

    static long modPow(long x, long n) {
        long res = 1L;
        while (n > 0) {
            if ((n & 1) == 1) {
                res = res * x % MOD;
            }
            x = x * x % MOD;
            n >>= 1;
        }
        return res;
    }

    //↑nCrをmod計算するために必要

    static int gcd(int n, int r) {
        return r == 0 ? n : gcd(r, n % r);
    }

    static long gcd(long n, long r) {
        return r == 0 ? n : gcd(r, n % r);
    }

    public static int upperDiv(int n,int m){
        return (n + m - 1)/m;
    }

    public static long upperDiv(long n,long m){
        return (n + m - 1)/m;
    }
    public static long upperDiv(long n,int m){
        return (n + m - 1)/m;
    }


    static <T> void swap(T[] x, int i, int j) {
        T t = x[i];
        x[i] = x[j];
        x[j] = t;
    }

    static void swap(int[] x, int i, int j) {
        int t = x[i];
        x[i] = x[j];
        x[j] = t;
    }

    public static void reverse(int[] x) {
        int l = 0;
        int r = x.length - 1;
        while (l < r) {
            int temp = x[l];
            x[l] = x[r];
            x[r] = temp;
            l++;
            r--;
        }
    }
    static <T> void reverse(T[] x, int s, int e) {
        int l = s;
        int r = e;
        while (l < r) {
            T temp = x[l];
            x[l] = x[r];
            x[r] = temp;
            l++;
            r--;
        }
    }

    public static void reverse(long[] x) {
        int l = 0;
        int r = x.length - 1;
        while (l < r) {
            long temp = x[l];
            x[l] = x[r];
            x[r] = temp;
            l++;
            r--;
        }
    }

    public static void reverse(int[] x, int s, int e) {
        int l = s;
        int r = e;
        while (l < r) {
            int temp = x[l];
            x[l] = x[r];
            x[r] = temp;
            l++;
            r--;
        }
    }

    static int length(int a) {
        int cou = 0;
        while (a != 0) {
            a /= 10;
            cou++;
        }
        return cou;
    }

    static int length(long a) {
        int cou = 0;
        while (a != 0) {
            a /= 10;
            cou++;
        }
        return cou;
    }

    static int cou(boolean[] a) {
        int res = 0;
        for (boolean b : a) {
            if (b) res++;
        }
        return res;
    }

    static int cou(String s, char c) {
        int res = 0;
        for (char ci : s.toCharArray()) {
            if (ci == c) res++;
        }
        return res;
    }

    static int countC2(char[][] a, char c) {
        int co = 0;
        for (int i = 0; i < a.length; i++)
            for (int j = 0; j < a[0].length; j++)
                if (a[i][j] == c) co++;
        return co;
    }

    static int countI(int[] a, int key) {
        int co = 0;
        for (int i = 0; i < a.length; i++)
            if (a[i] == key) co++;
        return co;
    }

    static int countI(int[][] a, int key) {
        int co = 0;
        for (int i = 0; i < a.length; i++)
            for (int j = 0; j < a[0].length; j++)
                if (a[i][j] == key) co++;
        return co;
    }

    static void fill(int[][] a, int v) {
        for (int i = 0; i < a.length; i++)
            for (int j = 0; j < a[0].length; j++)
                a[i][j] = v;
    }


    static void fill(long[][] a, long v) {
        for (int i = 0; i < a.length; i++)
            for (int j = 0; j < a[0].length; j++)
                a[i][j] = v;
    }

    static void fill(int[][][] a, int v) {
        for (int i = 0; i < a.length; i++)
            for (int j = 0; j < a[0].length; j++)
                for (int k = 0; k < a[0][0].length; k++)
                    a[i][j][k] = v;
    }

    static int max(int... a) {
        int res = Integer.MIN_VALUE;
        for (int i : a) {
            res = Math.max(res, i);
        }
        return res;
    }

    static long max(long... a) {
        long res = Long.MIN_VALUE;
        for (long i : a) {
            res = Math.max(res, i);
        }
        return res;
    }


    static int max(int[][] ar) {
        int res = Integer.MIN_VALUE;
        for (int i[] : ar)
            res = Math.max(res, max(i));
        return res;
    }

    static int min(int... a) {
        int res = Integer.MAX_VALUE;
        for (int i : a) {
            res = Math.min(res, i);
        }
        return res;
    }

    static long min(long... a) {
        long res = Long.MAX_VALUE;
        for (long i : a) {
            res = Math.min(res, i);
        }
        return res;
    }

    static int min(int[][] ar) {
        int res = Integer.MAX_VALUE;
        for (int i[] : ar)
            res = Math.min(res, min(i));
        return res;
    }

    static int sum(int[] a) {
        int cou = 0;
        for (int i : a)
            cou += i;
        return cou;
    }

    static int abs(int a) {
        return Math.abs(a);
    }


    static long abs(long a) {
        return Math.abs(a);
    }

    static class FastScanner {

        private BufferedReader reader = null;
        private StringTokenizer tokenizer = null;

        public FastScanner(InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
            tokenizer = null;
        }

        public String next() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        /*public String nextChar(){
            return (char)next()[0];
        }*/
        public String nextLine() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    return reader.readLine();
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }

            return tokenizer.nextToken("\n");
        }

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

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

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

        public int[] nextIntArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = nextInt();
            }
            return a;
        }

        public int[] nextIntArrayDec(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = nextInt() - 1;
            }
            return a;
        }

        public int[][] nextIntArray2(int h, int w) {
            int[][] a = new int[h][w];
            for (int hi = 0; hi < h; hi++) {
                for (int wi = 0; wi < w; wi++) {
                    a[hi][wi] = nextInt();
                }
            }
            return a;
        }

        public int[][] nextIntArray2Dec(int h, int w) {
            int[][] a = new int[h][w];
            for (int hi = 0; hi < h; hi++) {
                for (int wi = 0; wi < w; wi++) {
                    a[hi][wi] = nextInt() - 1;
                }
            }
            return a;
        }

        //複数の配列を受け取る
        public void nextIntArrays2ar(int[] a, int[] b) {
            for (int i = 0; i < a.length; i++) {
                a[i] = sc.nextInt();
                b[i] = sc.nextInt();
            }
        }

        public void nextIntArrays2arDec(int[] a, int[] b) {
            for (int i = 0; i < a.length; i++) {
                a[i] = sc.nextInt() - 1;
                b[i] = sc.nextInt() - 1;
            }
        }

        //複数の配列を受け取る
        public void nextIntArrays3ar(int[] a, int[] b, int[] c) {
            for (int i = 0; i < a.length; i++) {
                a[i] = sc.nextInt();
                b[i] = sc.nextInt();
                c[i] = sc.nextInt();
            }
        }

        //複数の配列を受け取る
        public void nextIntArrays3arDecLeft2(int[] a, int[] b, int[] c) {
            for (int i = 0; i < a.length; i++) {
                a[i] = sc.nextInt() - 1;
                b[i] = sc.nextInt() - 1;
                c[i] = sc.nextInt();
            }
        }

        public Integer[] nextIntegerArray(int n) {
            Integer[] a = new Integer[n];
            for (int i = 0; i < n; i++) {
                a[i] = nextInt();
            }
            return a;
        }

        public char[] nextCharArray(int n) {
            char[] a = next().toCharArray();

            return a;
        }

        public char[][] nextCharArray2(int h, int w) {
            char[][] a = new char[h][w];
            for (int i = 0; i < h; i++) {
                a[i] = next().toCharArray();
            }
            return a;
        }

        //スペースが入っている場合
        public char[][] nextCharArray2s(int h, int w) {
            char[][] a = new char[h][w];
            for (int i = 0; i < h; i++) {
                a[i] = nextLine().replace(" ", "").toCharArray();
            }
            return a;
        }

        public char[][] nextWrapCharArray2(int h, int w, char c) {
            char[][] a = new char[h + 2][w + 2];
            //char c = '*';
            int i;
            for (i = 0; i < w + 2; i++)
                a[0][i] = c;
            for (i = 1; i < h + 1; i++) {
                a[i] = (c + next() + c).toCharArray();
            }
            for (i = 0; i < w + 2; i++)
                a[h + 1][i] = c;
            return a;
        }

        //スペースが入ってる時用
        public char[][] nextWrapCharArray2s(int h, int w, char c) {
            char[][] a = new char[h + 2][w + 2];
            //char c = '*';
            int i;
            for (i = 0; i < w + 2; i++)
                a[0][i] = c;
            for (i = 1; i < h + 1; i++) {
                a[i] = (c + nextLine().replace(" ", "") + c).toCharArray();
            }
            for (i = 0; i < w + 2; i++)
                a[h + 1][i] = c;
            return a;
        }

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

        public long[][] nextLongArray2(int h, int w) {
            long[][] a = new long[h][w];
            for (int hi = 0; hi < h; hi++) {
                for (int wi = 0; wi < w; wi++) {
                    a[hi][wi] = nextLong();
                }
            }
            return a;
        }
    }
}