Problem: Vasya and Petya were tired of studying so they decided to play a game. Before the game begins Vasya looks at array a consisting of n integers. As soon as he remembers all elements of a the game begins. Vasya closes his eyes and Petya does q actions of one of two types:

1) Petya says 4 integers l1, r1, l2, r2 — boundaries of two non-intersecting segments. After that he swaps one random element from the [l1, r1] segment with another random element from the [l2, r2] segment.

2) Petya asks Vasya the sum of the elements of a in the [l, r] segment.

Vasya is a mathematician so he answers Petya the mathematical expectation of the sum of the elements in the segment.

Your task is to write a program which will answer the second type questions as Vasya would do it. In other words your program should print the mathematical expectation of the sum of the elements of a in the [l, r] segment for every second type query.

Input

The first line contains two integers n, q (2 ≤ n ≤ 105, 1 ≤ q ≤ 105) — the number of elements in the array and the number of queries you need to handle.

The second line contains n integers ai (1 ≤ ai ≤ 109) — elements of the array.

The next q lines contain Petya's actions of type 1 or 2.

If it is a type 1 action then the line contains 5 integers 1, l1, r1, l2, r2 (1 ≤ l1 ≤ r1 ≤ n, 1 ≤ l2 ≤ r2 ≤ n).

If it is a type 2 query then the line contains 3 integers 2, l, r (1 ≤ l ≤ r ≤ n).

It is guaranteed that there is at least one type 2 query and segments [l1, r1], [l2, r2] don't have common elements. 

Output

For each type 2 query print one real number — the mathematical expectation of the sum of elements in the segment.

Your answer will be considered correct if its absolute or relative error doesn't exceed 10 - 4 — formally, the answer is correct if <image> where x is jury's answer and y is yours.

Examples

Input

4 4
1 1 2 2
1 2 2 3 3
2 1 2
1 1 2 3 4
2 1 2


Output

3.0000000
3.0000000


Input

10 5
1 1 1 1 1 2 2 2 2 2
1 1 5 6 10
2 1 5
1 1 5 6 10
1 1 5 6 10
2 6 10


Output

6.0000000
8.0400000


Input

10 10
1 2 3 4 5 6 7 8 9 10
1 1 5 6 10
1 1 5 6 10
2 1 5
1 1 3 6 9
2 1 3
1 5 7 8 10
1 1 1 10 10
2 1 5
2 7 10
2 1 10


Output

23.0000000
14.0000000
28.0133333
21.5733333
55.0000000

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int n = 1 << 17;
double sum[n * 2], lazy_mul[n * 2], lazy_add[n * 2];
void push(int i, int l, int r) {
  if (lazy_mul[i] != 1 || lazy_add[i] != 0) {
    sum[i] = sum[i] * lazy_mul[i] + lazy_add[i] * (r - l);
    if (i < n) {
      for (int j : {i * 2, i * 2 + 1}) {
        lazy_mul[j] *= lazy_mul[i];
        lazy_add[j] *= lazy_mul[i];
        lazy_add[j] += lazy_add[i];
      }
    }
    lazy_mul[i] = 1;
    lazy_add[i] = 0;
  }
}
void fma(double mul, double add, int a, int b, int l = 0, int r = n,
         int i = 1) {
  push(i, l, r);
  if (a >= r || b <= l) return;
  if (a <= l && b >= r) {
    lazy_mul[i] = mul;
    lazy_add[i] = add;
    push(i, l, r);
    return;
  }
  int m = l + r >> 1;
  fma(mul, add, a, b, l, m, i * 2);
  fma(mul, add, a, b, m, r, i * 2 + 1);
  sum[i] = sum[i * 2] + sum[i * 2 + 1];
}
double querySum(int a, int b, int l = 0, int r = n, int i = 1) {
  push(i, l, r);
  if (a >= r || b <= l) return 0;
  if (a <= l && b >= r) {
    return sum[i];
  }
  int m = l + r >> 1;
  return querySum(a, b, l, m, i * 2) + querySum(a, b, m, r, i * 2 + 1);
}
int main() {
  fill_n(lazy_mul, n * 2, 1.);
  ios::sync_with_stdio(0);
  cin.tie(0);
  int n, q;
  cin >> n >> q;
  for (int i = 0; i < n; i++) {
    int a;
    cin >> a;
    fma(1, a, i, i + 1);
  }
  while (q--) {
    int type;
    cin >> type;
    if (type == 1) {
      int l1, r1, l2, r2;
      cin >> l1 >> r1 >> l2 >> r2;
      l1--, l2--;
      double e1 = querySum(l1, r1) / (r1 - l1);
      double e2 = querySum(l2, r2) / (r2 - l2);
      double p1 = 1. / (r1 - l1);
      fma(1 - p1, p1 * e2, l1, r1);
      double p2 = 1. / (r2 - l2);
      fma(1 - p2, p2 * e1, l2, r2);
    } else {
      int l, r;
      cin >> l >> r;
      l--;
      cout << setprecision(20) << querySum(l, r) << '\n';
    }
  }
}