This is an interactive problem.

After completing the last level of the enchanted temple, you received a powerful artifact of the 255th level. Do not rush to celebrate, because this artifact has a powerful rune that can be destroyed with a single spell s, which you are going to find. 

We define the spell as some non-empty string consisting only of the letters a and b.

At any time, you can cast an arbitrary non-empty spell t, and the rune on the artifact will begin to resist. Resistance of the rune is the edit distance between the strings that specify the casted spell t and the rune-destroying spell s.

[Edit distance](https://en.wikipedia.org/wiki/Levenshtein_distance) of two strings s and t is a value equal to the minimum number of one-character operations of replacing, inserting and deleting characters in s to get t. For example, the distance between ababa and aaa is 2, the distance between aaa and aba is 1, the distance between bbaba and abb is 3. The edit distance is 0 if and only if the strings are equal.

It is also worth considering that the artifact has a resistance limit — if you cast more than n + 2 spells, where n is the length of spell s, the rune will be blocked.

Thus, it takes n + 2 or fewer spells to destroy the rune that is on your artifact. Keep in mind that the required destructive spell s must also be counted among these n + 2 spells.

Note that the length n of the rune-destroying spell s is not known to you in advance. It is only known that its length n does not exceed 300.

Interaction

Interaction is happening through queries.

Each request consists of a single non-empty string t — the spell you want to cast. The length of string t should not exceed 300. Each string should consist only of the letters a and b.

In response to the query, you will get resistance runes — the edit distance between the strings that specify the casted spell t and the secret rune-destroying spell s. Remember that s contains only the letters a and b.

After breaking the rune, your program should end immediately. A rune is destroyed when you get a response with resistance 0. After receiving the value 0, your program should terminate normally.

In this problem interactor is not adaptive. This means that during any test the rune-destroying spell s does not change. 

If your query is invalid, -1 will be returned. After receiving this your program should immediately terminate normally (for example, by calling exit(0)), otherwise, the testing system may issue an arbitrary verdict.

If the number of spells exceeds limit (n + 2, where n is the length of the spell s, which is unknown to you), you will get the Wrong Answer verdict.

Your solution may receive the verdict Idleness Limit Exceeded if you don't output anything or forget to flush the output buffer.

To flush the output buffer, you need to do the following immediately after printing the query and the line end:

  * fflush(stdout) or cout.flush() in C++; 
  * System.out.flush() in Java; 
  * flush(output) in Pascal; 
  * stdout.flush() in Python; 
  * for other languages see documentation. 



Hacks

For hacks, use the following format:

In a single line print the string s (1 ≤ |s| ≤ 300) of letters a and b, which defines the rune-destroying spell.

The hacked solution will not have direct access to the unknown spell.

Example

Input



2

2

1

2

3

0

Output


aaa

aaab

abba

bba

abaaa

aabba
import java.util.*;
import java.io.*;
import java.io.FileWriter; 
import java.math.BigInteger;
import java.math.BigDecimal;
// Solution
 
public class Main 
{    
  public static void main (String[] argv) 
  {
	  new Main();
  } 
     
  
  boolean test = false;  
  final int[][] dirs8 = {{0,1}, {0,-1}, {-1,0}, {1,0}, {1,1},{1,-1},{-1,1},{-1,-1}};
  final int[][] dirs4 = {{0,1}, {0,-1}, {-1,0}, {1,0}};
  //final int MOD = 1000000007;  //998244353;
  final int MOD = 998244353;
  
  
  
  int[] fac;
  int[] ifac;
  int[] rfac;
  
  int[] pow2;
  
  int[] mobius;
  int[] sieve;
  int[][] factors;

  
 
  public Main()  {
	FastReader in = new FastReader(new BufferedReader(new InputStreamReader(System.in)));
	
     
    //FastReader in = new FastReader(new BufferedReader(new FileReader("Main.in")));   
    
    //int nt = in.nextInt();    
    int nt = 0;
    StringBuilder sb = new StringBuilder();
    
    System.out.println("a");
    System.out.flush();    
    int r = in.nextInt();
    if (r == 0) return;
    if (r == 300)
    {
        char[] t = new char[300];
        for (int i = 0; i < 300; i++) t[i] = 'b';
        System.out.println(new String(t));
        System.out.flush();
        in.nextInt();
        return;
    }
    
    int n = r + 1;
    char[] ans = new char[n];
    for (int i = 0; i < n; i++) ans[i] = 'a';
    
    System.out.println(new String(ans));
    System.out.flush();
    r = in.nextInt();
    if (r == 0) return;
    
    if (r == n) {
        --n;
        ans = new char[n];
        for (int i = 0; i < n; i++) ans[i] = 'b';
        System.out.println(new String(ans));
        System.out.flush();
        r = in.nextInt();
        return;
    }
    
    
    int nb = r;    // nb must be > 0
    
    for (int i = 0; i < n - 1; i++)
    {
        ans[i] = 'b';
        System.out.println(new String(ans));
        System.out.flush();
        int res = in.nextInt();
        if (res == 0) return;
        
        if (res < nb)
        {
            // this position in indeed 'b'
            --nb;
            if (nb == 0) break;
        }else {
            //this position should be a
            ans[i] = 'a';
        }
    }
    
    if (nb > 0) ans[n-1] = 'b';
    System.out.println(new String(ans));
    System.out.flush();
    in.nextInt();
    
    for (int iq = 0; iq < nt; iq++)
    {        
       n = in.nextInt();
       int t = in.nextInt();
       int[] a = new int[n];
       for (int i = 0; i < n; i++) a[i] = in.nextInt();
       
       long[] csum = new long[n+1];
       for (int i = 0; i < n; i++) csum[i+1] = csum[i] + a[i];
       
       if (csum[n] <= t)
       {
           sb.append("0\n");
           continue;
       }
       
       int[] maxp = new int[n];
       for (int i = 1; i < n; i++)
       {
           if (a[i] > a[maxp[i-1]])
               maxp[i] = i;
           else maxp[i] = maxp[i-1];
       }
       
       
       int skipID = 0;
       int lo = 1, hi = n;
       while (lo <= hi)
       {
           int mid = (lo + hi) / 2;
           if (csum[mid] <= t) {
               skipID = 0;
               lo = mid + 1;               
           }else if (csum[mid] - a[maxp[mid-1]] <= t)
           {
               //can finish
               lo = mid + 1;
               if (maxp[mid-1] < mid - 1)
                   skipID = maxp[mid-1] + 1; // + 1 to change to 1-based
           }else hi = mid - 1;
           
       }
       sb.append(skipID + "\n");
       //sb.append(cnt+"\n");
    }
    //System.out.print(sb);
    
  }
  
  //node:  1 2 .. n
  class TreeNbs {
      int n;
      int[][] edges;
      int[] deg;
      int[][] nbs;
      
      public TreeNbs(int n, int[][] edges)
      {
          this.n = n;
          this.edges = edges;
          deg = new int[n+1];
          nbs = new int[n+1][];
          
          for (int[] edge : edges)
          {
              int p = edge[0], q = edge[1];
              deg[p]++;
              deg[q]++;
          }
          
          for (int i = 1; i <= n; i++) {
             nbs[i] = new int[deg[i]];
             deg[i] = 0;
          }
          
          for (int[] edge : edges)
          {
              int p = edge[0], q = edge[1];
              nbs[p][deg[p]++] = q;
              nbs[q][deg[q]++] = p;
          }
      }
  }
  
  private long dist(long x0, long y0, long x1, long y1)
  {
      return abs(y0 - y1) + abs(x0 - x1);
  }
  
  class Point {
      int x, y;
      public Point(int x, int y)
      {
          this.x = x;
          this.y = y;
      }
  }

  
  class Edge{
      int p, q;
      boolean used;
      public Edge(int pp, int qq)
      {
          p = pp;
          q = qq;
          used = false;
      }      
  }
  
  class Node implements Comparable<Node>{
      int id;
      long gain;
      public Node(int id, long gain)
      {
          this.id = id;
          this.gain = gain;
      }
      
      @Override
      public int compareTo(Node o){
          return Long.compare(gain, o.gain);
      }
  }
  
  private long[][] matIdentity(int n)
  {
      long[][] a = new long[n][n];
      for (int i = 0; i < n; i++)
          a[i][i] = 1;
      return a;
  }
  private long[][] matPow(long[][] mat0, long p)
  {
      int n = mat0.length;
      long[][] ans = matIdentity(n);
      long[][] mat = matCopy(mat0);
      while (p > 0)
      {
          if (p % 2 == 1){
              ans = matMul(ans, mat);
          }
          
          p /= 2;
          mat = matMul(mat, mat);
      }
      return ans;
  }
  
  private long[][] matCopy(long[][] a)
  {
      int n = a.length;
      long[][] b = new long[n][n];
      for (int i = 0; i < n; i++)
          for (int j = 0; j < n; j++)
              b[i][j] = a[i][j];
      return b;
  }
  private long[][] matMul(long[][] a, long[][] b)
  {
      int n = a.length;
      
      long[][] c = new long[n][n];
      for (int i = 0; i < n; i++)
      {
          for (int j = 0; j < n; j++)
          {
              for (int k = 0; k < n; k++)
                  c[i][j] = (c[i][j] + a[i][k] * b[k][j]) % MOD;
          }
      }
      
      return c;
  }
  
  private long[] matMul(long[][] a, long[] b)
  {
      int n = a.length;
      
      long[] c = new long[n];
      for (int i = 0; i < n; i++)
      {
          for (int j = 0; j < n; j++)
              c[i] = (c[i] + a[i][j] * b[j]) % MOD;
      }
      
      return c;
  }
  
  class Mark implements Comparable<Mark> {
      int type, h;
      long x;
      public Mark(int h, long x, int type)
      {
         this.h = h;
         this.x = x;
         this.type = type;
      }      
      
      @Override
      public int compareTo(Mark o)
      {
          if (this.x == o.x) return type - o.type; // let end comes before start
          return Long.compare(x, o.x); 
      }
  }
  
  private boolean coLinear(int[] p, int[] q, int[] r)
  {
      return 1L * (p[1] - r[1]) * (q[0] - r[0]) == 1L * (q[1] - r[1]) * (p[0] - r[0]);
  }
  
  
  private void fill(char[] a, int lo, int c, char letter)
  {
      //System.out.println("fill " + lo + " " + c + " " + letter);
      for (int i = lo; i < lo + c; i++) a[i] = letter;
  }
  
  
  
  private int cntBitOne(String s){
      int c = 0, n = s.length();
      for (int i = 0; i < n; i++) 
          if (s.charAt(i) == '1') c++;
      return c;
  }
  
  class DSU {
      int n;
      int[] par;
      int[] sz;
      int nGroup;
      
      public DSU(int n)
      {
          this.n = n;
          par = new int[n];
          sz = new int[n];
          for (int i = 0;  i < n; i++){
              par[i] = i;
              sz[i] = 1;
          }
          nGroup = n;          
      }
      
      private boolean add(int p, int q) {
          int rp = find(p);
          int rq = find(q);
          if (rq == rp) return false;
          
          if (sz[rp] <= sz[rq]) {
              sz[rq] += sz[rp];
              par[rp] = rq;
          }else {
              sz[rp] += sz[rq];
              par[rq] = rp;
          }
          nGroup--;
          return true;
      }
      
      private int find(int p)
      {
          int r = p;
          while (par[r] != r) r = par[r];
          
          while (r != p) {
              int t = par[p];
              par[p] = r;
              p = t;
          }
          return r;
      }
      
  }
  
  
  // μ(n) = 1 if n is a square-free positive integer with an even number of prime factors. e.g.  6, 15
  // μ(n) = −1 if n is a square-free positive integer with an odd number of prime factors. e.g.  2, 3, 5, 2*3*5
  // μ(n) = 0 if n has a squared prime factor. e.g : 2*2,  3*3*5
  private void build_pow2_function(int n)
  {
      pow2 = new int[n+1];
       pow2[0] = 1;
       for (int i = 1; i <= n; i++) pow2[i] = (int)(1L * pow2[i-1] * 2 % MOD);
  }
  
  private void build_fac_function(int n)
  {
      fac = new int[n+1];
      fac[0] = 1;
      for (int i = 1; i <= n; i++)
          fac[i] = (int)(1L * fac[i-1] * i % MOD);
  }
  
  private void build_ifac_function(int n)
  {
      ifac = new int[n+1];
      ifac[0] = 1;
      for (int i = 1; i <= n; i++)
          ifac[i] = (int)(1L * ifac[i-1] * inv(i) % MOD);
  }
  
  private void build_sieve_function(int n)
  {
      sieve = new int[n+1];
      for (int i = 2; i <= n; i++)
        sieve[i] = i;
      for (int i = 2; i <= n; i++) 
      {
        if (sieve[i] == i){
            for (long j = 1L * i * i; j <= n; j += i)
                sieve[(int)j] = i;
        }
      }
  }
  
  private void build_mobius_function(int n)
  {
      mobius = new int[n+1];
      sieve = new int[n+1];
      factors = new int[n+1][];
      //for (int i = 1; i <= n; i++)factors[i] = new ArrayList<>();
      for (int i = 2; i <= n; i++)
        sieve[i] = i;
      for (int i = 2; i <= n; i++) 
      {
        if (sieve[i] == i){
            mobius[i] = -1;
            for (long j = 1L * i * i; j <= n; j += i)
                sieve[(int)j] = i;
        }
      }
      
      for (int i = 6; i <= n; i++)
      {
          if (sieve[i] != i) {
              int pre = i / sieve[i];
              if (pre % sieve[i] != 0)
                  mobius[i] = -mobius[pre];
          }
      }
      int[] sz = new int[n+1];
      long tot = 0;
      for (int i = 2; i <= n; i++) 
      {
          if (mobius[i] != 0)
          {
              for (int j = i * 2; j <= n; j += i) {                  
                  sz[j]++;
                  tot++;
              }                  
          }
      }
      for (int i = 2; i <= n; i++) {
          factors[i] = new int[sz[i]];
          sz[i] = 0;
      }
      
      
      for (int i = 2; i <= n; i++) 
      {
          if (mobius[i] != 0)
          {
              for (int j = i * 2; j <= n; j += i) {
                  factors[j][sz[j]++] = i;
                  //factors[j].add(i);
              }                  
          }
      }
      //System.out.println("tot  =  "  + tot);
  }
  
  private int[] build_z_function(String s)
  {
      int n = s.length();
      int[] zfun = new int[n];
      
      int l = -1, r = -1;
      for (int i = 1; i < n; i++)
      {
         // Set the start value
         if (i <= r)
            zfun[i] = Math.min(zfun[i-l], r - i + 1);
         
         while (i + zfun[i] < n && s.charAt(i + zfun[i]) == s.charAt(zfun[i])) 
             zfun[i]++;             
         
         if (i + zfun[i] - 1> r){
             l = i;
             r = i + zfun[i] - 1;
         }
      }
      
      if (test)
      {
          System.out.println("Z-function of " + s);
          for (int i = 0; i < n; i++) System.out.print(zfun[i] + " ");
          System.out.println();
      }
      return zfun;
  }
  
  class BIT {
      int[] bit;
      int n;
      
      public BIT(int n){
          this.n = n;
          bit = new int[n+1];
      }
      
      private int query(int p)
      {
          int sum = 0;
          for (; p > 0; p -= (p & (-p)))
             sum += bit[p];
      
          return sum;
      }
  
      private void add(int p, int val)
      {
         //System.out.println("add to BIT " + p);
         for (; p <= n; p += (p & (-p)))
            bit[p] += val;
      }
  
  
  }
  
  
  
  private List<Integer> getMinFactor(int sum)
  {
      List<Integer>  factors = new ArrayList<>();
      
               for (int sz = 2; sz <= sum / sz; sz++){
                   if (sum % sz == 0) {
                       factors.add(sz);
                       factors.add(sum / sz);
                   }
               }
               if (factors.size() == 0)
                   factors.add(sum);
          
      return factors;
  }
  
  /* Tree class */
  class Tree {
      int V = 0;
      int root = 0;
      List<Integer>[] nbs;
      int[][] timeRange;
      int[] subTreeSize;
      int t;
      boolean dump = false;
      
      public Tree(int V, int root)
      {
          if (dump) 
              System.out.println("build tree with size = " + V + ", root = " + root); 
          
          this.V = V;          
          this.root = root;
          nbs = new List[V];
          subTreeSize = new int[V];
          for (int i = 0; i < V; i++)
              nbs[i] = new ArrayList<>();
          
              
      }
      
      public void doneInput()
      {
          dfsEuler();
      }
      
      public void addEdge(int p, int q)
      {
          nbs[p].add(q);
          nbs[q].add(p);
      }
      
      private void dfsEuler()
      {
          timeRange = new int[V][2];          
          t = 1;
          dfs(root);           
      }
      
      private void dfs(int node)
      {
          if (dump)
              System.out.println("dfs on node " + node + ", at time " + t);
          timeRange[node][0] = t;
          
          for (int next : nbs[node]) {
              if (timeRange[next][0] == 0)
              {
                  ++t;
                  dfs(next);                  
              }
          }
          timeRange[node][1] = t;
          subTreeSize[node] = t - timeRange[node][0] + 1;
      }
      
      public List<Integer> getNeighbors(int p) {
          return nbs[p];
      }
      
      public int[] getSubTreeSize(){
          return subTreeSize;
      }
      
      public int[][] getTimeRange()
      {
          if (dump){
              for (int i = 0; i < V; i++){
                  System.out.println(i + ": " + timeRange[i][0] + " - " + timeRange[i][1]);
              }
          }
          return timeRange;
      }
      
  }
  
  /* segment tree */
  class SegTree {
      int[] a;
      int[] tree;
      int[] treeMin;
      int[] treeMax;
      int[] lazy;
      int n;
      boolean dump = false;
      
      public SegTree(int n)
      {
          if (dump)
              System.out.println("create segTree with size " + n);
          this.n = n;
          treeMin = new int[n*4];
          treeMax = new int[n*4];
          lazy = new int[n*4];
      }
      
      public SegTree(int n, int[] a) {
          this(n);
          this.a = a;
          buildTree(1, 0, n-1);          
      }
      
      private void buildTree(int node, int lo, int hi)
      {
          if (lo == hi) {
              tree[node] = lo;
              return;
          }
          
          int m = (lo + hi) / 2;
          buildTree(node * 2, lo, m);
          buildTree(node * 2 + 1, m + 1, hi);
          pushUp(node, lo, hi);
      }
      
      
      private void pushUp(int node, int lo, int hi)
      {
          if (lo >= hi) return;
          
          // note that, if we need to call pushUp on a node, then lazy[node] must be zero.
          
          //the true value is the value + lazy
          treeMin[node] = Math.min(treeMin[node * 2] + lazy[node * 2], treeMin[node * 2 + 1] + lazy[node * 2 + 1]);
          treeMax[node] = Math.max(treeMax[node * 2] + lazy[node * 2], treeMax[node * 2 + 1] + lazy[node * 2 + 1]);
          // add combine fcn
      }
      
      private void pushDown(int node, int lo, int hi)
      {
          if (lazy[node] == 0) return;
          
          int lz = lazy[node];
          lazy[node] = 0;          
          
          
          treeMin[node] += lz;
          treeMax[node] += lz;     
          
          if (lo == hi) return;
          
          int mid = (lo + hi) / 2;
          lazy[node * 2] += lz;
          lazy[node * 2 + 1] += lz;
      }
      
      public int rangeQueryMax(int fr, int to)
      {
          return rangeQueryMax(1, 0, n-1, fr, to);
      }
      
      public int rangeQueryMax(int node, int lo, int hi, int fr, int to)
      {
          if (lo == fr && hi == to)
              return treeMax[node] + lazy[node];
          
          int mid = (lo + hi) / 2;
          pushDown(node, lo, hi);
          
          if (to <= mid) {
              return rangeQueryMax(node * 2, lo, mid, fr, to);
          }else if (fr > mid)
              return rangeQueryMax(node * 2 + 1, mid + 1, hi, fr, to);
          else {
              return Math.max(rangeQueryMax(node * 2, lo, mid, fr, mid),
                              rangeQueryMax(node * 2 + 1, mid + 1, hi, mid + 1, to));              
          }
      }
      
      public int rangeQueryMin(int fr, int to)
      {
          return rangeQueryMin(1, 0, n-1, fr, to);
      }
      
      public int rangeQueryMin(int node, int lo, int hi, int fr, int to)
      {
          if (lo == fr && hi == to)
              return treeMin[node] + lazy[node];
          
          int mid = (lo + hi) / 2;
          pushDown(node, lo, hi);
          
          if (to <= mid) {
              return rangeQueryMin(node * 2, lo, mid, fr, to);
          }else if (fr > mid)
              return rangeQueryMin(node * 2 + 1, mid + 1, hi, fr, to);
          else {
              return Math.min(rangeQueryMin(node * 2, lo, mid, fr, mid),
                              rangeQueryMin(node * 2 + 1, mid + 1, hi, mid + 1, to));              
          }
      }
      
       public void rangeUpdate(int fr, int to, int delta){
           rangeUpdate(1, 0, n-1, fr, to, delta);
       }
       
       
      public void rangeUpdate(int node, int lo, int hi, int fr, int to, int delta){
          pushDown(node, lo, hi);
          if (fr == lo && to == hi)
          {
              lazy[node] = delta;
              return;
          }
          
          int m = (lo + hi) / 2;
          if (to <= m) 
              rangeUpdate(node * 2, lo, m, fr, to, delta);
          else if (fr > m)
              rangeUpdate(node * 2 + 1, m + 1, hi, fr, to, delta);
          else  {
              rangeUpdate(node *  2, lo, m, fr, m, delta);
              rangeUpdate(node * 2 + 1, m + 1, hi, m + 1, to, delta);              
          }
          
          // re-set the in-variant
          pushUp(node, lo, hi);
      }
      
      
      
      public int query(int node, int lo, int hi, int fr, int to)
      {
          if (fr == lo && to == hi)
              return tree[node];
          
          int m = (lo + hi) / 2;
          if (to <= m) 
              return  query(node * 2, lo, m, fr, to);
          else if (fr > m)
              return query(node * 2 + 1, m + 1, hi, fr, to);
          
          int lid = query(node * 2, lo, m, fr, m);
          int rid = query(node * 2 + 1, m + 1, hi, m + 1, to);
          return a[lid] >= a[rid] ? lid : rid;
      }
      
      
  }
  
  
  private long inv(long v)
  {
      return pow(v, MOD-2);
  }
  
  private long pow(long v, long p)
  {
      long ans = 1;
      while (p > 0)
      {
          if (p % 2 == 1)
              ans = ans * v % MOD;
          v = v * v % MOD;
          p = p / 2;
      }
      return ans;
  }
  
  private double dist(double x, double y, double xx, double yy)
  {
      return Math.sqrt((xx - x) * (xx - x) + (yy - y) * (yy - y));
  }
  
 
  
 
  private int mod_add(int a, int b) {
      int v = a + b;
      if (v >= MOD) v -= MOD;
      return v;
  }
  
  
  private long overlap(int x1, int y1, int x2, int y2, int x3, int y3, int x4, int y4) {
      if (x1 > x3) return overlap(x3, y3, x4, y4, x1, y1, x2, y2);
      
      if (x3 > x2 || y4 < y1 || y3 > y2) return 0L;
      
      //(x3, ?, x2, ?)
      int yL = Math.max(y1, y3);
      int yH = Math.min(y2, y4); 
      int xH = Math.min(x2, x4);
      
      return f(x3, yL, xH, yH);
  }
  //return #black cells in rectangle
  private long f(int x1, int y1, int x2, int y2) {
      long dx = 1L + x2 - x1;
      long dy = 1L + y2 - y1;
      if (dx % 2 == 0 || dy % 2 == 0 || (x1 + y1) % 2 == 0) 
          return 1L * dx * dy / 2;
      return 1L * dx * dy / 2 + 1;
  }
  
  private int distM(int x, int y, int xx, int yy) {
      return abs(x - xx) + abs(y - yy);
  }
  
  private boolean less(int x, int y, int xx, int yy) {
      return x < xx || y > yy;
  }
  
  private int mul(int x, int y) {
      return (int)(1L * x * y % MOD);
  }
  
  
 
  
  private int nBit1(int v) {
      int v0 = v;
      int c = 0;
      while (v != 0) {
          ++c;
          v = v & (v - 1);
      }
      return c;
  }
  
  private long abs(long v) {
      return v > 0 ? v : -v;
  }
  
  private int abs(int v) {
      return v > 0 ? v : -v;
  }
  
  private int common(int v) {
      int c = 0;
      while (v != 1) {
          v = (v >>> 1);
          ++c;
      }
      
      return c;
  }
  
  private void reverse(char[] a, int i, int j) {
      while (i < j) {
          swap(a, i++, j--);
      }
  }
  
  private void swap(char[] a, int i, int j) {
      char t = a[i];
      a[i] = a[j];
      a[j] = t;
  }
  
  private int gcd(int x, int y) {
      if (y == 0) return x;
      return gcd(y, x % y);
  }
  private long gcd(long x, long y) {
      if (y == 0) return x;
      return gcd(y, x % y);
  }
  private int max(int a, int b) {
      return a >  b ? a : b;
  }
  
  private long max(long a, long b) {
      return a >  b ? a : b;
  }
  
  private int min(int a, int b) {
      return a >  b ? b : a;
  }
  
  private long min(long a, long b) {
      return a >  b ? b : a;
  }
  
  static class FastReader
    {
        BufferedReader br;
        StringTokenizer st;
 
        public FastReader(BufferedReader in)
        {            
            br = in;
        }
 
        String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    String line = br.readLine();
                    if (line == null || line.length() == 0) return "";
                    st = new StringTokenizer(line);
                }
                catch (IOException  e)
                {
                    return "";
                    //e.printStackTrace();
                }
            }
            return st.nextToken();
        }
 
        int nextInt()
        {
            return Integer.parseInt(next());
        }
 
        long nextLong()
        {
            return Long.parseLong(next());
        }
 
        double nextDouble()
        {
            return Double.parseDouble(next());
        }
 
        String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                return null;
                //e.printStackTrace();
            }
            return str;
        }
    }
}