#include <bits/stdc++.h>
using namespace std;
template <typename T>
inline void ckmax(T& x, T y) {
  x = (y > x ? y : x);
}
template <typename T>
inline void ckmin(T& x, T y) {
  x = (y < x ? y : x);
}
namespace Fread {
const int SIZE = 1 << 21;
char buf[SIZE], *S, *T;
inline char getchar() {
  if (S == T) {
    T = (S = buf) + fread(buf, 1, SIZE, stdin);
    if (S == T) return EOF;
  }
  return *S++;
}
}  // namespace Fread
namespace Fwrite {
const int SIZE = 1 << 21;
char buf[SIZE], *S = buf, *T = buf + SIZE;
inline void flush() {
  fwrite(buf, 1, S - buf, stdout);
  S = buf;
}
inline void putchar(char c) {
  *S++ = c;
  if (S == T) flush();
}
struct NTR {
  ~NTR() { flush(); }
} ztr;
}  // namespace Fwrite
namespace Fastio {
struct Reader {
  template <typename T>
  Reader& operator>>(T& x) {
    char c = Fread ::getchar();
    T f = 1;
    while (c < '0' || c > '9') {
      if (c == '-') f = -1;
      c = Fread ::getchar();
    }
    x = 0;
    while (c >= '0' && c <= '9') {
      x = x * 10 + (c - '0');
      c = Fread ::getchar();
    }
    x *= f;
    return *this;
  }
  Reader& operator>>(char& c) {
    c = Fread ::getchar();
    while (c == '\n' || c == ' ') c = Fread ::getchar();
    return *this;
  }
  Reader& operator>>(char* str) {
    int len = 0;
    char c = Fread ::getchar();
    while (c == '\n' || c == ' ') c = Fread ::getchar();
    while (c != '\n' && c != ' ') {
      str[len++] = c;
      c = Fread ::getchar();
    }
    str[len] = '\0';
    return *this;
  }
  Reader() {}
} cin;
const char endl = '\n';
struct Writer {
  template <typename T>
  Writer& operator<<(T x) {
    if (x == 0) {
      Fwrite ::putchar('0');
      return *this;
    }
    if (x < 0) {
      Fwrite ::putchar('-');
      x = -x;
    }
    static int sta[45];
    int top = 0;
    while (x) {
      sta[++top] = x % 10;
      x /= 10;
    }
    while (top) {
      Fwrite ::putchar(sta[top] + '0');
      --top;
    }
    return *this;
  }
  Writer& operator<<(char c) {
    Fwrite ::putchar(c);
    return *this;
  }
  Writer& operator<<(char* str) {
    int cur = 0;
    while (str[cur]) Fwrite ::putchar(str[cur++]);
    return *this;
  }
  Writer& operator<<(const char* str) {
    int cur = 0;
    while (str[cur]) Fwrite ::putchar(str[cur++]);
    return *this;
  }
  Writer() {}
} cout;
}  // namespace Fastio
const int MAXN = 2e5;
int n;
void solve_case() {
  Fastio ::cin >> n;
  int ans = n;
  for (int i = n - 1; i >= 1; --i) {
    ans = (ans + i + 1) / 2;
  }
  Fastio ::cout << ans << Fastio ::endl;
  ans = n;
  for (int i = n - 1; i >= 1; --i) {
    Fastio ::cout << ans << " " << i << Fastio ::endl;
    ans = (ans + i + 1) / 2;
  }
}
int main() {
  int T;
  Fastio ::cin >> T;
  while (T--) {
    solve_case();
  }
  return 0;
}

### Prompt

In cpp, your task is to solve the following problem:

Numbers 1, 2, 3, ... n (each integer from 1 to n once) are written on a board. In one operation you can erase any two numbers a and b from the board and write one integer (a + b)/(2) rounded up instead.

You should perform the given operation n - 1 times and make the resulting number that will be left on the board as small as possible. 

For example, if n = 4, the following course of action is optimal:

  1. choose a = 4 and b = 2, so the new number is 3, and the whiteboard contains [1, 3, 3]; 
  2. choose a = 3 and b = 3, so the new number is 3, and the whiteboard contains [1, 3]; 
  3. choose a = 1 and b = 3, so the new number is 2, and the whiteboard contains [2]. 



It's easy to see that after n - 1 operations, there will be left only one number. Your goal is to minimize it.

Input

The first line contains one integer t (1 ≤ t ≤ 1000) — the number of test cases.

The only line of each test case contains one integer n (2 ≤ n ≤ 2 ⋅ 10^5) — the number of integers written on the board initially.

It's guaranteed that the total sum of n over test cases doesn't exceed 2 ⋅ 10^5.

Output

For each test case, in the first line, print the minimum possible number left on the board after n - 1 operations. Each of the next n - 1 lines should contain two integers — numbers a and b chosen and erased in each operation.

Example

Input


1
4


Output


2
2 4
3 3
3 1

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
template <typename T>
inline void ckmax(T& x, T y) {
  x = (y > x ? y : x);
}
template <typename T>
inline void ckmin(T& x, T y) {
  x = (y < x ? y : x);
}
namespace Fread {
const int SIZE = 1 << 21;
char buf[SIZE], *S, *T;
inline char getchar() {
  if (S == T) {
    T = (S = buf) + fread(buf, 1, SIZE, stdin);
    if (S == T) return EOF;
  }
  return *S++;
}
}  // namespace Fread
namespace Fwrite {
const int SIZE = 1 << 21;
char buf[SIZE], *S = buf, *T = buf + SIZE;
inline void flush() {
  fwrite(buf, 1, S - buf, stdout);
  S = buf;
}
inline void putchar(char c) {
  *S++ = c;
  if (S == T) flush();
}
struct NTR {
  ~NTR() { flush(); }
} ztr;
}  // namespace Fwrite
namespace Fastio {
struct Reader {
  template <typename T>
  Reader& operator>>(T& x) {
    char c = Fread ::getchar();
    T f = 1;
    while (c < '0' || c > '9') {
      if (c == '-') f = -1;
      c = Fread ::getchar();
    }
    x = 0;
    while (c >= '0' && c <= '9') {
      x = x * 10 + (c - '0');
      c = Fread ::getchar();
    }
    x *= f;
    return *this;
  }
  Reader& operator>>(char& c) {
    c = Fread ::getchar();
    while (c == '\n' || c == ' ') c = Fread ::getchar();
    return *this;
  }
  Reader& operator>>(char* str) {
    int len = 0;
    char c = Fread ::getchar();
    while (c == '\n' || c == ' ') c = Fread ::getchar();
    while (c != '\n' && c != ' ') {
      str[len++] = c;
      c = Fread ::getchar();
    }
    str[len] = '\0';
    return *this;
  }
  Reader() {}
} cin;
const char endl = '\n';
struct Writer {
  template <typename T>
  Writer& operator<<(T x) {
    if (x == 0) {
      Fwrite ::putchar('0');
      return *this;
    }
    if (x < 0) {
      Fwrite ::putchar('-');
      x = -x;
    }
    static int sta[45];
    int top = 0;
    while (x) {
      sta[++top] = x % 10;
      x /= 10;
    }
    while (top) {
      Fwrite ::putchar(sta[top] + '0');
      --top;
    }
    return *this;
  }
  Writer& operator<<(char c) {
    Fwrite ::putchar(c);
    return *this;
  }
  Writer& operator<<(char* str) {
    int cur = 0;
    while (str[cur]) Fwrite ::putchar(str[cur++]);
    return *this;
  }
  Writer& operator<<(const char* str) {
    int cur = 0;
    while (str[cur]) Fwrite ::putchar(str[cur++]);
    return *this;
  }
  Writer() {}
} cout;
}  // namespace Fastio
const int MAXN = 2e5;
int n;
void solve_case() {
  Fastio ::cin >> n;
  int ans = n;
  for (int i = n - 1; i >= 1; --i) {
    ans = (ans + i + 1) / 2;
  }
  Fastio ::cout << ans << Fastio ::endl;
  ans = n;
  for (int i = n - 1; i >= 1; --i) {
    Fastio ::cout << ans << " " << i << Fastio ::endl;
    ans = (ans + i + 1) / 2;
  }
}
int main() {
  int T;
  Fastio ::cin >> T;
  while (T--) {
    solve_case();
  }
  return 0;
}

```