#include <bits/stdc++.h>
using namespace std;
FILE* _fin = stdin;
FILE* _fout = stdout;
int _min(int a, int b) { return a <= b ? a : b; }
long long _min(long long a, long long b) { return a <= b ? a : b; }
int _max(int a, int b) { return a >= b ? a : b; }
long long _max(long long a, long long b) { return a >= b ? a : b; }
void zero(int* data, int n) { memset(data, 0, sizeof(int) * n); }
void zero(long long* data, int n) { memset(data, 0, sizeof(long long) * n); }
void zero(unsigned long long* data, int n) {
  memset(data, 0, sizeof(unsigned long long) * n);
}
void zero(char* data, int n) { memset(data, 0, sizeof(char) * n); }
char readc() {
  char var;
  fscanf(_fin, "%c", &var);
  return var;
}
int readi() {
  int var;
  fscanf(_fin, "%d", &var);
  return var;
}
double readlf() {
  double var;
  fscanf(_fin, "%lf", &var);
  return var;
}
long long readll() {
  long long var;
  fscanf(_fin, "%lld", &var);
  return var;
}
void repread(int* data, int n) {
  for (int i = 0; i < n; ++i) data[i] = readi();
}
void repread(long long* data, int n) {
  for (int i = 0; i < n; ++i) data[i] = readll();
}
int reads(char* str, int maxsize) {
  for (;;) {
    if (fgets(str, maxsize, _fin) == NULL) break;
    if (str[0] != '\n' && str[0] != '\r') break;
  }
  int slen = strlen(str);
  if (slen == 0) return 0;
  if (str[slen - 1] == '\n' || str[slen - 1] == '\r') str[--slen] = 0;
  return slen;
}
long long gcd(long long a, long long b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
long long lcm(long long a, long long b) {
  long long g = gcd(a, b);
  return (a / g) * b;
}
void reverse(char* data, int n) {
  int k = n >> 1;
  for (int i = 0; i < k; ++i) {
    char tmp = data[i];
    data[i] = data[n - i - 1];
    data[n - i - 1] = tmp;
  }
}
void reverse(int* data, int n) {
  int k = n >> 1;
  for (int i = 0; i < k; ++i) {
    int tmp = data[i];
    data[i] = data[n - i - 1];
    data[n - i - 1] = tmp;
  }
}
void reverse(long long* data, int n) {
  int k = n >> 1;
  for (int i = 0; i < k; ++i) {
    long long tmp = data[i];
    data[i] = data[n - i - 1];
    data[n - i - 1] = tmp;
  }
}
struct Veci {
  int* data;
  int size;
  int n;
};
void init(Veci* t, int size) {
  t->data = (int*)malloc(sizeof(int) * size);
  t->size = size;
  t->n = 0;
}
void resize(Veci* t) {
  int ns = t->size * 1.2f;
  t->data = (int*)realloc(t->data, sizeof(int) * ns);
  t->size = ns;
}
void add(Veci* t, int val) {
  if (t->n >= t->size) resize(t);
  int k = t->n;
  t->data[k] = val;
  t->n = k + 1;
}
void free(Veci* t) { free(t->data); }
struct Vecll {
  long long* data;
  int size;
  int n;
};
void init(Vecll* t, int size) {
  t->data = (long long*)malloc(sizeof(long long) * size);
  t->size = size;
  t->n = 0;
}
void resize(Vecll* t) {
  int ns = t->size * 1.2f;
  t->data = (long long*)realloc(t->data, sizeof(long long) * ns);
  t->size = ns;
}
void add(Vecll* t, long long val) {
  if (t->n >= t->size) resize(t);
  int k = t->n;
  t->data[k] = val;
  t->n = k + 1;
}
void free(Vecll* t) { free(t->data); }
struct Vecs {
  char** data;
  int size;
  int n;
};
void init(Vecs* t, int size) {
  t->data = (char**)malloc(sizeof(char*) * size);
  t->size = size;
  t->n = 0;
}
void resize(Vecs* t) {
  int ns = t->size * 1.2f;
  t->data = (char**)realloc(t->data, sizeof(char*) * ns);
  t->size = ns;
}
void add(Vecs* t, char* val) {
  if (t->n >= t->size) resize(t);
  int k = t->n;
  t->data[k] = val;
  t->n = k + 1;
}
void free(Vecs* t) { free(t->data); }
int ispali(int* a, int* b, int n) {
  for (int i = 0; i < n; ++i) {
    if (a[i] != b[n - i - 1]) {
      return 0;
    }
  }
  return 1;
}
int ispalc(char* a, char* b, int n) {
  for (int i = 0; i < n; ++i) {
    if (a[i] != b[n - i - 1]) {
      return 0;
    }
  }
  return 1;
}
struct Pairi {
  int x, y;
};
int cmp_Pairi(const void* _a, const void* _b) {
  Pairi* a = (Pairi*)_a;
  Pairi* b = (Pairi*)_b;
  if (a->x < b->x)
    return -1;
  else {
    if (a->x == b->x) {
      if (a->y == b->y) return 0;
      if (a->y < b->y)
        return -1;
      else
        return 1;
    } else {
      return 1;
    }
  }
}
void sort_Pairi(Pairi* d, int n) { qsort(d, n, sizeof(Pairi), cmp_Pairi); }
struct Pairlf {
  double x, y;
};
int cmp_Pairlf(const void* _a, const void* _b) {
  Pairlf* a = (Pairlf*)_a;
  Pairlf* b = (Pairlf*)_b;
  if (a->x < b->x)
    return -1;
  else {
    if (a->x == b->x) {
      if (a->y == b->y) return 0;
      if (a->y < b->y)
        return -1;
      else
        return 1;
    } else {
      return 1;
    }
  }
}
void sort_Pairlf(Pairlf* d, int n) { qsort(d, n, sizeof(Pairlf), cmp_Pairlf); }
int cmp_Str(const void* _a, const void* _b) {
  char* a = *((char**)_a);
  char* b = *((char**)_b);
  return strcmp(a, b);
}
void sort_Str(char** str, int n) { qsort(str, n, sizeof(char*), cmp_Str); }
long long expmod(long long x, long long n, long long m) {
  long long ans = 1;
  for (; n;) {
    if (n & 1) ans = (ans * x) % m;
    x = (x * x) % m;
    n >>= 1;
  }
  return ans;
}
long long combmod(long long n, long long k, long long m) {
  long long ret = 1;
  long long div = 1;
  for (long long i = 0; i < k; ++i) {
    ret = (ret * (n - i) % m) % m;
    div = (div * (i + 1)) % m;
  }
  div = expmod(div, m - 2, m) % m;
  return (ret * div) % m;
}
int next_perm(int* data, int n) {
  int rootidx = -1;
  for (int i = n - 2; i >= 0; --i) {
    if (data[i] < data[i + 1]) {
      rootidx = i;
      break;
    }
  }
  if (rootidx == -1) return 0;
  int ceilingidx = rootidx + 1;
  for (int i = rootidx + 2; i < n; ++i) {
    if (data[i] > data[rootidx] && data[i] < data[ceilingidx]) {
      ceilingidx = i;
    }
  }
  {
    int t = data[rootidx];
    data[rootidx] = data[ceilingidx];
    data[ceilingidx] = t;
  };
  std::sort(&data[rootidx + 1], &data[rootidx + 1] + n - rootidx - 1);
  return 1;
}
int count_digits(long long a) {
  int k = 0;
  for (;;) {
    if (a == 0) break;
    k++;
    a /= 10;
  }
  return k;
}
int bs_exists(int* data, int n, int val) {
  int left = 0;
  int right = n - 1;
  for (; left < right;) {
    int mid = (left + right + 1) >> 1;
    if (data[mid] <= val)
      left = mid;
    else
      right = mid - 1;
  }
  return right;
}
long long simple_factorial(int x) {
  long long f = 1.0;
  for (int i = 0; i < x; ++i) {
    f *= (i + 1);
  }
  return f;
}
unsigned long long djb2(char* data, int n) {
  unsigned long long h = 5381;
  for (int i = 0; i < n; ++i) h = (h << 5) + h + data[i];
  return h;
}
struct Hashcount {
  int* count;
  unsigned long long* keys;
  int size_bits;
};
void init(Hashcount* h, int size_bits) {
  h->size_bits = size_bits;
  int size = 1 << h->size_bits;
  h->count = (int*)malloc(sizeof(int) * size);
  zero(h->count, size);
  h->keys = (unsigned long long*)malloc(sizeof(unsigned long long) * size);
  zero(h->keys, size);
}
int set(Hashcount* h, unsigned long long key) {
  int index = (key * 2654435761) >> (64 - h->size_bits);
  int size = 1 << h->size_bits;
  for (int i = 0; i < size; i++) {
    if (h->keys[index] == key) {
      h->count[index]++;
      return index;
    }
    if (h->keys[index] == 0) {
      h->count[index] = 1;
      h->keys[index] = key;
      return index;
    }
    index++;
    index &= size - 1;
  }
  return -1;
}
int get(Hashcount* h, unsigned long long key) {
  int index = (key * 2654435761) >> (64 - h->size_bits);
  int size = 1 << h->size_bits;
  for (int i = 0; i < size; i++) {
    if (h->keys[index] == key) {
      return h->count[index];
    }
    if (h->keys[index] == 0) return 0;
    index++;
    index &= size - 1;
  }
  return 0;
}
int sub(Hashcount* h, unsigned long long key) {
  int index = (key * 2654435761) >> (64 - h->size_bits);
  int size = 1 << h->size_bits;
  for (int i = 0; i < size; i++) {
    if (h->keys[index] == key) {
      --h->count[index];
      if (h->count[index] < 0) h->count[index] = 0;
      return h->count[index];
    }
    if (h->keys[index] == 0) return 0;
    index++;
    index &= size - 1;
  }
  return 0;
}
const long long MOD = 1e9 + 7;
int main() {
  {
    _fin = fopen("input.txt", "r");
    if (_fin == NULL) _fin = stdin;
  };
  int t = readi();
  for (int _t = 0; _t < t; ++_t) {
    int n = readi();
    static char s[201];
    static char prevs[201];
    static int a[201];
    repread(a, n);
    int minlenrequired = 1;
    for (int i = 0; i < n; ++i) {
      minlenrequired = _max(minlenrequired, a[i]);
    }
    minlenrequired++;
    int m = 0;
    char c = 'a';
    for (int i = 0; i < minlenrequired; ++i) {
      prevs[m] = c;
      s[m] = c;
      m++;
    }
    s[m] = 0;
    prevs[m] = 0;
    printf(s);
    printf("\n");
    for (int i = 0; i < n; ++i) {
      if (a[i] != 0) {
        if (prevs[a[i]] == 'a')
          s[a[i]] = 'b';
        else
          s[a[i]] = 'a';
        printf(s);
        printf("\n");
      } else {
        if (prevs[0] == 'a')
          s[0] = 'b';
        else
          s[0] = 'a';
        printf(s);
        printf("\n");
      }
      for (int j = 0; j < m; ++j) prevs[j] = s[j];
    }
  }
  return 0;
}

### Prompt

Please formulate a CPP solution to the following problem:

The length of the longest common prefix of two strings s = s_1 s_2 … s_n and t = t_1 t_2 … t_m is defined as the maximum integer k (0 ≤ k ≤ min(n,m)) such that s_1 s_2 … s_k equals t_1 t_2 … t_k.

Koa the Koala initially has n+1 strings s_1, s_2, ..., s_{n+1}.

For each i (1 ≤ i ≤ n) she calculated a_i — the length of the longest common prefix of s_i and s_{i+1}.

Several days later Koa found these numbers, but she couldn't remember the strings.

So Koa would like to find some strings s_1, s_2, ..., s_{n+1} which would have generated numbers a_1, a_2, ..., a_n. Can you help her?

If there are many answers print any. We can show that answer always exists for the given constraints. 

Input

Each test contains multiple test cases. The first line contains t (1 ≤ t ≤ 100) — the number of test cases. Description of the test cases follows.

The first line of each test case contains a single integer n (1 ≤ n ≤ 100) — the number of elements in the list a.

The second line of each test case contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ 50) — the elements of a.

It is guaranteed that the sum of n over all test cases does not exceed 100.

Output

For each test case:

Output n+1 lines. In the i-th line print string s_i (1 ≤ |s_i| ≤ 200), consisting of lowercase Latin letters. Length of the longest common prefix of strings s_i and s_{i+1} has to be equal to a_i.

If there are many answers print any. We can show that answer always exists for the given constraints.

Example

Input


4
4
1 2 4 2
2
5 3
3
1 3 1
3
0 0 0


Output


aeren
ari
arousal
around
ari
monogon
monogamy
monthly
kevinvu
kuroni
kurioni
korone
anton
loves
adhoc
problems

Note

In the 1-st test case one of the possible answers is s = [aeren, ari, arousal, around, ari].

Lengths of longest common prefixes are:

  * Between \color{red}{a}eren and \color{red}{a}ri → 1 
  * Between \color{red}{ar}i and \color{red}{ar}ousal → 2 
  * Between \color{red}{arou}sal and \color{red}{arou}nd → 4 
  * Between \color{red}{ar}ound and \color{red}{ar}i → 2 

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
FILE* _fin = stdin;
FILE* _fout = stdout;
int _min(int a, int b) { return a <= b ? a : b; }
long long _min(long long a, long long b) { return a <= b ? a : b; }
int _max(int a, int b) { return a >= b ? a : b; }
long long _max(long long a, long long b) { return a >= b ? a : b; }
void zero(int* data, int n) { memset(data, 0, sizeof(int) * n); }
void zero(long long* data, int n) { memset(data, 0, sizeof(long long) * n); }
void zero(unsigned long long* data, int n) {
  memset(data, 0, sizeof(unsigned long long) * n);
}
void zero(char* data, int n) { memset(data, 0, sizeof(char) * n); }
char readc() {
  char var;
  fscanf(_fin, "%c", &var);
  return var;
}
int readi() {
  int var;
  fscanf(_fin, "%d", &var);
  return var;
}
double readlf() {
  double var;
  fscanf(_fin, "%lf", &var);
  return var;
}
long long readll() {
  long long var;
  fscanf(_fin, "%lld", &var);
  return var;
}
void repread(int* data, int n) {
  for (int i = 0; i < n; ++i) data[i] = readi();
}
void repread(long long* data, int n) {
  for (int i = 0; i < n; ++i) data[i] = readll();
}
int reads(char* str, int maxsize) {
  for (;;) {
    if (fgets(str, maxsize, _fin) == NULL) break;
    if (str[0] != '\n' && str[0] != '\r') break;
  }
  int slen = strlen(str);
  if (slen == 0) return 0;
  if (str[slen - 1] == '\n' || str[slen - 1] == '\r') str[--slen] = 0;
  return slen;
}
long long gcd(long long a, long long b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
long long lcm(long long a, long long b) {
  long long g = gcd(a, b);
  return (a / g) * b;
}
void reverse(char* data, int n) {
  int k = n >> 1;
  for (int i = 0; i < k; ++i) {
    char tmp = data[i];
    data[i] = data[n - i - 1];
    data[n - i - 1] = tmp;
  }
}
void reverse(int* data, int n) {
  int k = n >> 1;
  for (int i = 0; i < k; ++i) {
    int tmp = data[i];
    data[i] = data[n - i - 1];
    data[n - i - 1] = tmp;
  }
}
void reverse(long long* data, int n) {
  int k = n >> 1;
  for (int i = 0; i < k; ++i) {
    long long tmp = data[i];
    data[i] = data[n - i - 1];
    data[n - i - 1] = tmp;
  }
}
struct Veci {
  int* data;
  int size;
  int n;
};
void init(Veci* t, int size) {
  t->data = (int*)malloc(sizeof(int) * size);
  t->size = size;
  t->n = 0;
}
void resize(Veci* t) {
  int ns = t->size * 1.2f;
  t->data = (int*)realloc(t->data, sizeof(int) * ns);
  t->size = ns;
}
void add(Veci* t, int val) {
  if (t->n >= t->size) resize(t);
  int k = t->n;
  t->data[k] = val;
  t->n = k + 1;
}
void free(Veci* t) { free(t->data); }
struct Vecll {
  long long* data;
  int size;
  int n;
};
void init(Vecll* t, int size) {
  t->data = (long long*)malloc(sizeof(long long) * size);
  t->size = size;
  t->n = 0;
}
void resize(Vecll* t) {
  int ns = t->size * 1.2f;
  t->data = (long long*)realloc(t->data, sizeof(long long) * ns);
  t->size = ns;
}
void add(Vecll* t, long long val) {
  if (t->n >= t->size) resize(t);
  int k = t->n;
  t->data[k] = val;
  t->n = k + 1;
}
void free(Vecll* t) { free(t->data); }
struct Vecs {
  char** data;
  int size;
  int n;
};
void init(Vecs* t, int size) {
  t->data = (char**)malloc(sizeof(char*) * size);
  t->size = size;
  t->n = 0;
}
void resize(Vecs* t) {
  int ns = t->size * 1.2f;
  t->data = (char**)realloc(t->data, sizeof(char*) * ns);
  t->size = ns;
}
void add(Vecs* t, char* val) {
  if (t->n >= t->size) resize(t);
  int k = t->n;
  t->data[k] = val;
  t->n = k + 1;
}
void free(Vecs* t) { free(t->data); }
int ispali(int* a, int* b, int n) {
  for (int i = 0; i < n; ++i) {
    if (a[i] != b[n - i - 1]) {
      return 0;
    }
  }
  return 1;
}
int ispalc(char* a, char* b, int n) {
  for (int i = 0; i < n; ++i) {
    if (a[i] != b[n - i - 1]) {
      return 0;
    }
  }
  return 1;
}
struct Pairi {
  int x, y;
};
int cmp_Pairi(const void* _a, const void* _b) {
  Pairi* a = (Pairi*)_a;
  Pairi* b = (Pairi*)_b;
  if (a->x < b->x)
    return -1;
  else {
    if (a->x == b->x) {
      if (a->y == b->y) return 0;
      if (a->y < b->y)
        return -1;
      else
        return 1;
    } else {
      return 1;
    }
  }
}
void sort_Pairi(Pairi* d, int n) { qsort(d, n, sizeof(Pairi), cmp_Pairi); }
struct Pairlf {
  double x, y;
};
int cmp_Pairlf(const void* _a, const void* _b) {
  Pairlf* a = (Pairlf*)_a;
  Pairlf* b = (Pairlf*)_b;
  if (a->x < b->x)
    return -1;
  else {
    if (a->x == b->x) {
      if (a->y == b->y) return 0;
      if (a->y < b->y)
        return -1;
      else
        return 1;
    } else {
      return 1;
    }
  }
}
void sort_Pairlf(Pairlf* d, int n) { qsort(d, n, sizeof(Pairlf), cmp_Pairlf); }
int cmp_Str(const void* _a, const void* _b) {
  char* a = *((char**)_a);
  char* b = *((char**)_b);
  return strcmp(a, b);
}
void sort_Str(char** str, int n) { qsort(str, n, sizeof(char*), cmp_Str); }
long long expmod(long long x, long long n, long long m) {
  long long ans = 1;
  for (; n;) {
    if (n & 1) ans = (ans * x) % m;
    x = (x * x) % m;
    n >>= 1;
  }
  return ans;
}
long long combmod(long long n, long long k, long long m) {
  long long ret = 1;
  long long div = 1;
  for (long long i = 0; i < k; ++i) {
    ret = (ret * (n - i) % m) % m;
    div = (div * (i + 1)) % m;
  }
  div = expmod(div, m - 2, m) % m;
  return (ret * div) % m;
}
int next_perm(int* data, int n) {
  int rootidx = -1;
  for (int i = n - 2; i >= 0; --i) {
    if (data[i] < data[i + 1]) {
      rootidx = i;
      break;
    }
  }
  if (rootidx == -1) return 0;
  int ceilingidx = rootidx + 1;
  for (int i = rootidx + 2; i < n; ++i) {
    if (data[i] > data[rootidx] && data[i] < data[ceilingidx]) {
      ceilingidx = i;
    }
  }
  {
    int t = data[rootidx];
    data[rootidx] = data[ceilingidx];
    data[ceilingidx] = t;
  };
  std::sort(&data[rootidx + 1], &data[rootidx + 1] + n - rootidx - 1);
  return 1;
}
int count_digits(long long a) {
  int k = 0;
  for (;;) {
    if (a == 0) break;
    k++;
    a /= 10;
  }
  return k;
}
int bs_exists(int* data, int n, int val) {
  int left = 0;
  int right = n - 1;
  for (; left < right;) {
    int mid = (left + right + 1) >> 1;
    if (data[mid] <= val)
      left = mid;
    else
      right = mid - 1;
  }
  return right;
}
long long simple_factorial(int x) {
  long long f = 1.0;
  for (int i = 0; i < x; ++i) {
    f *= (i + 1);
  }
  return f;
}
unsigned long long djb2(char* data, int n) {
  unsigned long long h = 5381;
  for (int i = 0; i < n; ++i) h = (h << 5) + h + data[i];
  return h;
}
struct Hashcount {
  int* count;
  unsigned long long* keys;
  int size_bits;
};
void init(Hashcount* h, int size_bits) {
  h->size_bits = size_bits;
  int size = 1 << h->size_bits;
  h->count = (int*)malloc(sizeof(int) * size);
  zero(h->count, size);
  h->keys = (unsigned long long*)malloc(sizeof(unsigned long long) * size);
  zero(h->keys, size);
}
int set(Hashcount* h, unsigned long long key) {
  int index = (key * 2654435761) >> (64 - h->size_bits);
  int size = 1 << h->size_bits;
  for (int i = 0; i < size; i++) {
    if (h->keys[index] == key) {
      h->count[index]++;
      return index;
    }
    if (h->keys[index] == 0) {
      h->count[index] = 1;
      h->keys[index] = key;
      return index;
    }
    index++;
    index &= size - 1;
  }
  return -1;
}
int get(Hashcount* h, unsigned long long key) {
  int index = (key * 2654435761) >> (64 - h->size_bits);
  int size = 1 << h->size_bits;
  for (int i = 0; i < size; i++) {
    if (h->keys[index] == key) {
      return h->count[index];
    }
    if (h->keys[index] == 0) return 0;
    index++;
    index &= size - 1;
  }
  return 0;
}
int sub(Hashcount* h, unsigned long long key) {
  int index = (key * 2654435761) >> (64 - h->size_bits);
  int size = 1 << h->size_bits;
  for (int i = 0; i < size; i++) {
    if (h->keys[index] == key) {
      --h->count[index];
      if (h->count[index] < 0) h->count[index] = 0;
      return h->count[index];
    }
    if (h->keys[index] == 0) return 0;
    index++;
    index &= size - 1;
  }
  return 0;
}
const long long MOD = 1e9 + 7;
int main() {
  {
    _fin = fopen("input.txt", "r");
    if (_fin == NULL) _fin = stdin;
  };
  int t = readi();
  for (int _t = 0; _t < t; ++_t) {
    int n = readi();
    static char s[201];
    static char prevs[201];
    static int a[201];
    repread(a, n);
    int minlenrequired = 1;
    for (int i = 0; i < n; ++i) {
      minlenrequired = _max(minlenrequired, a[i]);
    }
    minlenrequired++;
    int m = 0;
    char c = 'a';
    for (int i = 0; i < minlenrequired; ++i) {
      prevs[m] = c;
      s[m] = c;
      m++;
    }
    s[m] = 0;
    prevs[m] = 0;
    printf(s);
    printf("\n");
    for (int i = 0; i < n; ++i) {
      if (a[i] != 0) {
        if (prevs[a[i]] == 'a')
          s[a[i]] = 'b';
        else
          s[a[i]] = 'a';
        printf(s);
        printf("\n");
      } else {
        if (prevs[0] == 'a')
          s[0] = 'b';
        else
          s[0] = 'a';
        printf(s);
        printf("\n");
      }
      for (int j = 0; j < m; ++j) prevs[j] = s[j];
    }
  }
  return 0;
}

```