#include <bits/stdc++.h>
using namespace std;
const int MAXN = 12;
const int MAXR = 1;
const int MAXC = 1;
const int MAXBITS = 64;
const int INF = (int)1e9;
int dx[] = {-1, 0, 1, 0};
int dy[] = {0, 1, 0, -1};
priority_queue<int, vector<int>, greater<int>> q1;
priority_queue<int, vector<int>, less<int>> q2;
void l() { ; }
int arr[MAXN];
string s;
bool c1() {
  for (int i = 0; i < 12; ++i) {
    if (s[i] == 'X') return true;
  }
  return false;
}
bool c2() {
  for (int i = 0; i < 6; ++i) {
    int idx = i;
    bool ans = true;
    for (int j = 0; j < 2; ++j) {
      if (s[idx] != 'X') {
        ans = false;
        break;
      }
      idx += 6;
    }
    if (ans) {
      return true;
    }
  }
  return false;
}
bool c3() {
  for (int i = 0; i < 4; ++i) {
    int idx = i;
    bool ans = true;
    for (int j = 0; j < 3; ++j) {
      if (s[idx] != 'X') {
        ans = false;
        break;
      }
      idx += 4;
    }
    if (ans) {
      return true;
    }
  }
  return false;
}
bool c4() {
  for (int i = 0; i < 3; ++i) {
    int idx = i;
    bool ans = true;
    for (int j = 0; j < 4; ++j) {
      if (s[idx] != 'X') {
        ans = false;
        break;
      }
      idx += 3;
    }
    if (ans) {
      return true;
    }
  }
  return false;
}
bool c6() {
  for (int i = 0; i < 2; ++i) {
    int idx = i;
    bool ans = true;
    for (int j = 0; j < 6; ++j) {
      if (s[idx] != 'X') {
        ans = false;
        break;
      }
      idx += 2;
    }
    if (ans) {
      return true;
    }
  }
  return false;
}
bool c12() {
  for (int i = 0; i < 12; ++i) {
    if (s[i] != 'X') return false;
  }
  return true;
}
void printAns() {
  l();
  ;
  bool isp1, isp2, isp3, isp4, isp6, isp12;
  isp1 = isp2 = isp3 = isp4 = isp6 = isp12 = false;
  int cnt = 0;
  isp1 = c1();
  isp2 = c2();
  isp3 = c3();
  isp4 = c4();
  isp6 = c6();
  isp12 = c12();
  if (isp1) cnt++;
  if (isp2) cnt++;
  if (isp3) cnt++;
  if (isp4) cnt++;
  if (isp6) cnt++;
  if (isp12) cnt++;
  cout << cnt << " ";
  if (isp1) {
    cout << "1x12"
         << " ";
  }
  if (isp2) {
    cout << "2x6"
         << " ";
  }
  if (isp3) {
    cout << "3x4"
         << " ";
  }
  if (isp4) {
    cout << "4x3"
         << " ";
  }
  if (isp6) {
    cout << "6x2"
         << " ";
  }
  if (isp12) {
    cout << "12x1"
         << " ";
  }
  cout << "\n";
  l();
}
int main(void) {
  ios::sync_with_stdio(false);
  cin.tie(NULL);
  int t;
  cin >> t;
  while (t--) {
    cin >> s;
    printAns();
  }
  return 0;
}
