#include <bits/stdc++.h>
using namespace std;
template <class T>
inline void gmin(T &x, const T &y) {
  if (x > y) x = y;
}
template <class T>
inline void gmax(T &x, const T &y) {
  if (x < y) x = y;
}
const int BufferSize = 1 << 16;
char buffer[BufferSize], *Bufferhead, *Buffertail;
bool Terminal;
inline char Getchar() {
  if (Bufferhead == Buffertail) {
    int l = fread(buffer, 1, BufferSize, stdin);
    if (!l) {
      Terminal = 1;
      return 0;
    }
    Buffertail = (Bufferhead = buffer) + l;
  }
  return *Bufferhead++;
}
template <class T>
inline bool read(T &x) {
  x = 0;
  char c = Getchar(), rev = 0;
  while (c < '0' || c > '9') {
    c = Getchar();
    rev |= c == '-';
    if (Terminal) return 0;
  }
  while (c >= '0' && c <= '9') x = x * 10 + c - '0', c = Getchar();
  if (c == '.') {
    c = Getchar();
    double t = 0.1;
    while (c >= '0' && c <= '9')
      x = x + (c - '0') * t, c = Getchar(), t = t / 10;
  }
  x = rev ? -x : x;
  return 1;
}
template <class T1, class T2>
inline bool read(T1 &x, T2 &y) {
  return read(x) & read(y);
}
template <class T1, class T2, class T3>
inline bool read(T1 &x, T2 &y, T3 &z) {
  return read(x) & read(y) & read(z);
}
template <class T1, class T2, class T3, class T4>
inline bool read(T1 &x, T2 &y, T3 &z, T4 &w) {
  return read(x) & read(y) & read(z) & read(w);
}
inline bool reads(char *x) {
  char c = Getchar();
  while (c < 33 || c > 126) {
    c = Getchar();
    if (Terminal) return 0;
  }
  while (c >= 33 && c <= 126) (*x++) = c, c = Getchar();
  *x = 0;
  return 1;
}
template <class T>
inline void print(T x, const char c = '\n') {
  if (!x) {
    putchar('0');
    putchar(c);
    return;
  }
  if (x < 0) putchar('-'), x = -x;
  int m = 0, a[20];
  while (x) a[m++] = x % 10, x /= 10;
  while (m--) putchar(a[m] + '0');
  putchar(c);
}
const int inf = 0x3f3f3f3f;
const int N = 2005, M = 100005, mod = 998244353;
template <class T, class S>
inline void ch(T &x, const S y) {
  x = (x + y) % mod;
}
inline int exp(int x, int y, const int mod = ::mod) {
  int ans = 1;
  while (y) {
    if (y & 1) ans = (long long)ans * x % mod;
    x = (long long)x * x % mod;
    y >>= 1;
  }
  return ans;
}
int n, m, f[2][N][11], g[2][N][11], fac[N], ifac[N];
vector<int> a, b;
char str[15];
inline int calc(int x, int k) {
  if (!x) return !k;
  return (long long)fac[x + k - 1] * ifac[x - 1] % mod;
}
int Main(int argv) {
  read(n);
  for (int i = 1; i <= n; i++) {
    reads(str);
    int t = 0;
    for (int j = 0; j < strlen(str); j++)
      if (j & 1)
        t = (t + 11 - str[j] + '0') % 11;
      else
        t = (t + str[j] - '0') % 11;
    if (strlen(str) & 1)
      a.push_back(t);
    else
      b.push_back(t);
  }
  n = a.size();
  m = b.size();
  f[0][0][0] = 1;
  for (int i = 0; i < n; i++) {
    memset(f[i + 1 & 1], 0, sizeof(f[i + 1 & 1]));
    for (int j = 0; j <= (n + 1) / 2 && j <= i; j++)
      for (int k = 0; k < 11; k++) {
        if (!f[i & 1][j][k]) continue;
        ch(f[i + 1 & 1][j + 1][(k + a[i]) % 11], f[i & 1][j][k]);
        ch(f[i + 1 & 1][j][(k + 11 - a[i]) % 11], f[i & 1][j][k]);
      }
  }
  for (int i = 0; i < 11; i++) g[0][0][i] = f[n & 1][(n + 1) / 2][i];
  for (int i = 0; i < m; i++) {
    memset(g[i + 1 & 1], 0, sizeof(g[i + 1 & 1]));
    for (int j = 0; j <= i; j++)
      for (int k = 0; k < 11; k++) {
        if (!g[i & 1][j][k]) continue;
        ch(g[i + 1 & 1][j + 1][(k + b[i]) % 11], g[i & 1][j][k]);
        ch(g[i + 1 & 1][j][(k + 11 - b[i]) % 11], g[i & 1][j][k]);
      }
  }
  int L = n / 2 + 1, R = n - n / 2, ans = 0;
  for (int j = 0; j <= m; j++)
    ch(ans, (long long)g[m & 1][j][0] * calc(L, j) % mod * calc(R, m - j));
  ans = (long long)ans * fac[(n + 1) / 2] % mod * fac[n / 2] % mod;
  print(ans);
  return 0;
}
void clear() {
  memset(f, 0, sizeof(f));
  memset(g, 0, sizeof(g));
  a.clear();
  b.clear();
}
int main() {
  int n = 2000;
  fac[0] = 1;
  for (int i = 1; i <= n; i++) fac[i] = (long long)fac[i - 1] * i % mod;
  ifac[n] = exp(fac[n], mod - 2);
  for (int i = n; i; i--) ifac[i - 1] = (long long)ifac[i] * i % mod;
  int T;
  scanf("%d", &T);
  for (int i = 1; i <= T; i++) Main(i), clear();
  return 0;
}
