#include <bits/stdc++.h>
using namespace std;
bool sortbyfir(const pair<int, int> &a, const pair<int, int> &b) {
  if (a.first == b.first) return a.second > b.second;
  return a.first < b.first;
}
bool sortbysec(const pair<int, int> &a, const pair<int, int> &b) {
  if (a.second == b.second) return b.first > a.first;
  return (a.second < b.second);
}
bool sr(const pair<int, int> &a, const pair<int, int> &b) {
  if (a.first == b.first)
    return a.second > b.second;
  else
    return a.first < b.first;
}
bool compmx(int a, int b) { return (a < b); }
long long int binaryToDecimal(string n) {
  string num = n;
  long long int dec_value = 0;
  long long int base = 1;
  for (int i = num.length() - 1; i >= 0; i--) {
    if (num[i] == '1') dec_value += base;
    base = base * 2;
  }
  return dec_value;
}
string decimalToBinary(long long int n) {
  string s = bitset<64>(n).to_string();
  const auto loc1 = s.find('1');
  if (loc1 != string::npos) return s.substr(loc1);
  return "0";
}
long long int gcd(long long int a, long long int b) {
  if (b == 0)
    return a;
  else
    return gcd(b, a % b);
}
long long int lcm(long long int a, long long int b) {
  return (a / gcd(a, b)) * b;
}
bool is_prime(long long int x) {
  if (x == 1) return false;
  if (x == 2 || x == 3) return true;
  for (long long int i = 2; i * i <= x; i++) {
    if (x % i == 0) return false;
  }
  return true;
}
bool isp(string str) {
  int l = 0, h = str.length() - 1;
  while (h > l)
    if (str[l++] != str[h--]) return false;
  return true;
}
long long int power(long long int a, long long int b) {
  long long int res = 1ll;
  while (b > 0) {
    if (b % 2ll) res = (res * a) % 1000000007;
    ;
    a = (a * a) % 1000000007;
    ;
    b /= 2ll;
  }
  return res;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  long long int t;
  cin >> t;
  while (t--) {
    long long int n;
    cin >> n;
    cout << n << endl;
    for (long long int i = 0; i < n; i++) cout << i + 1 << " ";
    cout << "\n";
    ;
  }
  return 0;
}

### Prompt

Your challenge is to write a CPP solution to the following problem:

There are n bags with candies, initially the i-th bag contains i candies. You want all the bags to contain an equal amount of candies in the end. 

To achieve this, you will:

  * Choose m such that 1 ≤ m ≤ 1000

  * Perform m operations. In the j-th operation, you will pick one bag and add j candies to all bags apart from the chosen one.




Your goal is to find a valid sequence of operations after which all the bags will contain an equal amount of candies. 

  * It can be proved that for the given constraints such a sequence always exists.

  * You don't have to minimize m.

  * If there are several valid sequences, you can output any.

Input

Each test contains multiple test cases.

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

The first and only line of each test case contains one integer n (2 ≤ n≤ 100). 

Output

For each testcase, print two lines with your answer. 

In the first line print m (1≤ m ≤ 1000) — the number of operations you want to take. 

In the second line print m positive integers a_1, a_2, ..., a_m (1 ≤ a_i ≤ n), where a_j is the number of bag you chose on the j-th operation.

Example

Input


2
2
3


Output


1
2
5
3 3 3 1 2

Note

In the first case, adding 1 candy to all bags except of the second one leads to the arrangement with [2, 2] candies.

In the second case, firstly you use first three operations to add 1+2+3=6 candies in total to each bag except of the third one, which gives you [7, 8, 3]. Later, you add 4 candies to second and third bag, so you have [7, 12, 7], and 5 candies to first and third bag — and the result is [12, 12, 12].

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
bool sortbyfir(const pair<int, int> &a, const pair<int, int> &b) {
  if (a.first == b.first) return a.second > b.second;
  return a.first < b.first;
}
bool sortbysec(const pair<int, int> &a, const pair<int, int> &b) {
  if (a.second == b.second) return b.first > a.first;
  return (a.second < b.second);
}
bool sr(const pair<int, int> &a, const pair<int, int> &b) {
  if (a.first == b.first)
    return a.second > b.second;
  else
    return a.first < b.first;
}
bool compmx(int a, int b) { return (a < b); }
long long int binaryToDecimal(string n) {
  string num = n;
  long long int dec_value = 0;
  long long int base = 1;
  for (int i = num.length() - 1; i >= 0; i--) {
    if (num[i] == '1') dec_value += base;
    base = base * 2;
  }
  return dec_value;
}
string decimalToBinary(long long int n) {
  string s = bitset<64>(n).to_string();
  const auto loc1 = s.find('1');
  if (loc1 != string::npos) return s.substr(loc1);
  return "0";
}
long long int gcd(long long int a, long long int b) {
  if (b == 0)
    return a;
  else
    return gcd(b, a % b);
}
long long int lcm(long long int a, long long int b) {
  return (a / gcd(a, b)) * b;
}
bool is_prime(long long int x) {
  if (x == 1) return false;
  if (x == 2 || x == 3) return true;
  for (long long int i = 2; i * i <= x; i++) {
    if (x % i == 0) return false;
  }
  return true;
}
bool isp(string str) {
  int l = 0, h = str.length() - 1;
  while (h > l)
    if (str[l++] != str[h--]) return false;
  return true;
}
long long int power(long long int a, long long int b) {
  long long int res = 1ll;
  while (b > 0) {
    if (b % 2ll) res = (res * a) % 1000000007;
    ;
    a = (a * a) % 1000000007;
    ;
    b /= 2ll;
  }
  return res;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  long long int t;
  cin >> t;
  while (t--) {
    long long int n;
    cin >> n;
    cout << n << endl;
    for (long long int i = 0; i < n; i++) cout << i + 1 << " ";
    cout << "\n";
    ;
  }
  return 0;
}

```