Problem: You are given an array a of n integers.

You want to make all elements of a equal to zero by doing the following operation exactly three times:

  * Select a segment, for each number in this segment we can add a multiple of len to it, where len is the length of this segment (added integers can be different). 



It can be proven that it is always possible to make all elements of a equal to zero.

Input

The first line contains one integer n (1 ≤ n ≤ 100 000): the number of elements of the array.

The second line contains n elements of an array a separated by spaces: a_1, a_2, ..., a_n (-10^9 ≤ a_i ≤ 10^9).

Output

The output should contain six lines representing three operations.

For each operation, print two lines:

  * The first line contains two integers l, r (1 ≤ l ≤ r ≤ n): the bounds of the selected segment.

  * The second line contains r-l+1 integers b_l, b_{l+1}, ..., b_r (-10^{18} ≤ b_i ≤ 10^{18}): the numbers to add to a_l, a_{l+1}, …, a_r, respectively; b_i should be divisible by r - l + 1.

Example

Input


4
1 3 2 4


Output


1 1 
-1
3 4
4 2
2 4
-3 -6 -6

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
#pragma GCC optimize(2)
#pragma GCC optimize("Ofast,inline")
using namespace std;
namespace Base {
inline char gc(void) {
  static char buf[100000], *p1 = buf, *p2 = buf;
  return p1 == p2 && (p2 = (p1 = buf) + fread(buf, 1, 100000, stdin), p1 == p2)
             ? EOF
             : *p1++;
}
template <class T>
inline void read(T &x) {
  T flag = (T)1;
  x = 0;
  static char ch = getchar();
  for (; ch > '9' || ch < '0'; ch = getchar()) flag = ch == '-' ? -1 : 1;
  for (; ch >= '0' && ch <= '9'; ch = getchar())
    x = (x << 1) + (x << 3) + (ch & 15);
  x *= flag;
  return;
}
inline void readstr(string &x) {
  x = "";
  static char ch;
  while (isspace(ch = getchar()))
    ;
  while (x += ch, !isspace(ch = getchar()))
    ;
}
inline void readstr(char *s) {
  do *s = getchar();
  while ((*s == ' ') || (*s == '\n') || (*s == '\r'));
  do *(++s) = getchar();
  while ((~*s) && (*s != ' ') && (*s != '\n') && (*s != '\r'));
  *s = 0;
  return;
}
inline void printstr(string x, int num = 0, char ch = '\n') {
  for (int i = num; i < x.size(); ++i) putchar(x[i]);
  putchar(ch);
}
inline void readch(char &x) {
  while (isspace(x = getchar()))
    ;
}
char pf[100000], *o1 = pf, *o2 = pf + 100000;
template <class T>
inline void println(T x, char c = '\n') {
  if (x < 0)
    (o1 == o2 ? fwrite(pf, 1, 100000, stdout), *(o1 = pf)++ = 45 : *o1++ = 45),
        x = -x;
  static char s[15], *b;
  b = s;
  if (!x) *b++ = 48;
  for (; x; *b++ = x % 10 + 48, x /= 10)
    ;
  for (; b-- != s; (o1 == o2          ? fwrite(pf, 1, 100000, stdout),
                    *(o1 = pf)++ = *b : *o1++ = *b))
    ;
  (o1 == o2 ? fwrite(pf, 1, 100000, stdout), *(o1 = pf)++ = c : *o1++ = c);
}
template <class T>
inline void write(T x) {
  if (x < 0) putchar('-'), x = -x;
  if (x > 9) write(x / 10);
  putchar(x % 10 + '0');
  return;
}
template <class T>
inline void writeln(T x) {
  write(x);
  puts("");
}
template <class T>
inline void writeln(T x, char c) {
  write(x);
  putchar(c);
}
template <class T>
inline void writeln(char c, T x) {
  putchar(c);
  write(x);
}
template <class T>
inline void chkmax(T &x, const T y) {
  x > y ? x = x : x = y;
}
template <class T>
inline void chkmin(T &x, const T y) {
  x < y ? x = x : x = y;
}
template <class T>
inline T max(const T &x, const T &y, const T &z) {
  return x > y ? (x > z ? x : z) : (y > z ? y : z);
}
inline void file(string str) {
  freopen((str + ".in").c_str(), "r", stdin);
  freopen((str + ".out").c_str(), "w", stdout);
}
struct Vector {
  double x, y;
  Vector(double _x = 0, double _y = 0) : x(_x), y(_y) {}
  inline Vector Vary(void) { return Vector(x, -y); }
  inline bool operator<(const Vector &rhs) const {
    return x == rhs.x ? y < rhs.y : x < rhs.x;
  }
  inline Vector operator-(const Vector &rhs) const {
    return Vector(x - rhs.x, y - rhs.y);
  }
  inline Vector operator+(const Vector &rhs) const {
    return Vector(x + rhs.x, y + rhs.y);
  }
  inline Vector operator*(const double &rhs) const {
    return Vector(x * rhs, y * rhs);
  }
  inline Vector operator/(const double &rhs) const {
    return Vector(x / rhs, y / rhs);
  }
  inline Vector operator*(const Vector &rhs) const {
    return Vector(x * rhs.x - y * rhs.y, x * rhs.y + y * rhs.x);
  }
};
}  // namespace Base
using namespace Base;
const int Maxn = 1e5 + 5;
int n;
long long a[Maxn];
signed main(void) {
  read(n);
  for (int i = 1; i <= n; i++) read(a[i]);
  puts("1 1");
  writeln(-a[1]);
  a[1] = 0;
  if (n == 1) {
    puts("1 1\n 0\n 1 1\n 0");
    return 0;
  }
  writeln(2, ' '), writeln(n);
  for (int i = 2; i <= n; i++)
    writeln(a[i] * (long long)(n - 1), " \n"[i == n]);
  writeln(1, ' '), writeln(n);
  for (int i = 1; i <= n; i++) writeln(-a[i] * (long long)n, " \n"[i == n]);
  return 0;
}