Problem: Write a program which manipulates a sequence $A$ = {$a_0, a_1, ..., a_{n-1}$} with the following operations:

* $update(s, t, x)$: change $a_s, a_{s+1}, ..., a_t$ to $x$.
* $getSum(s, t)$: print the sum of $a_s, a_{s+1}, ..., a_t$.



Note that the initial values of $a_i ( i = 0, 1, ..., n-1 )$ are 0.

Constraints

* $1 ≤ n ≤ 100000$
* $1 ≤ q ≤ 100000$
* $0 ≤ s ≤ t < n$
* $-1000 ≤ x ≤ 1000$

Input


$n$ $q$
$query_1$
$query_2$
:
$query_q$


In the first line, $n$ (the number of elements in $A$) and $q$ (the number of queries) are given. Then, $i$-th query $query_i$ is given in the following format:


0 $s$ $t$ $x$


or


1 $s$ $t$


The first digit represents the type of the query. '0' denotes $update(s, t, x)$ and '1' denotes $find(s, t)$.

Output

For each $getSum$ query, print the sum in a line.

Example

Input

6 7
0 1 3 1
0 2 4 -2
1 0 5
1 0 1
0 3 5 3
1 3 4
1 0 5


Output

-5
1
6
8

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
//#include <boost/multiprecision/cpp_int.hpp>
//using multiInt = boost::multiprecision::cpp_int;

using ll = long long int;
using ld = long double;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
template <typename Q_type>
using smaller_queue = priority_queue<Q_type, vector<Q_type>, greater<Q_type>>;

const int MOD_TYPE = 2;
const ll MOD = (MOD_TYPE == 1 ? (ll)(1e9 + 7) : 998244353);
const int INF = (int)1e9;
const ll LINF = (ll)4e18;
const ld DINF = 1e12;
const ld PI = acos(-1.0);
const ld EPS = 1e-11;

#define REP(i, m, n) for (ll i = m; i < (ll)(n); ++i)
#define rep(i, n) REP(i, 0, n)
#define MP make_pair
#define MT make_tuple
#define YES(n) cout << ((n) ? "YES" : "NO") << endl
#define Yes(n) cout << ((n) ? "Yes" : "No") << endl
#define Possible(n) cout << ((n) ? "Possible" : "Impossible") << endl
#define possible(n) cout << ((n) ? "possible" : "impossible") << endl
#define Yay(n) cout << ((n) ? "Yay!" : ":(") << endl
#define all(v) v.begin(), v.end()
#define NP(v) next_permutation(all(v))
#define dbg(x) cerr << #x << ":" << x << endl;

vector<int> Dx = {0, 0, -1, 1, -1, 1, -1, 1, 0};
vector<int> Dy = {1, -1, 0, 0, -1, -1, 1, 1, 0};

template <typename T, typename E>
struct SegmentTree
{
  using F = function<T(T, T)>;
  using G = function<T(T, E)>;
  using H = function<E(E, E)>;
  int n, height;
  F f;
  G g;
  H h;
  T ti;
  E ei;
  vector<T> dat;
  vector<E> laz;
  SegmentTree(F f, G g, H h, T ti, E ei) : f(f), g(g), h(h), ti(ti), ei(ei) {}

  void init(int n_)
  {
    n = 1;
    height = 0;
    while (n < n_)
      n <<= 1, height++;
    dat.assign(2 * n, ti);
    laz.assign(2 * n, ei);
  }

  void build(const vector<T> &v)
  {
    int n_ = v.size();
    init(n_);
    for (int i = 0; i < n_; i++)
      dat[n + i] = v[i];
    for (int i = n - 1; i; i--)
      dat[i] = f(dat[(i << 1) | 0], dat[(i << 1) | 1]);
  }

  inline T reflect(int k)
  {
    return laz[k] == ei ? dat[k] : g(dat[k], laz[k]);
  }

  inline void propagate(int k)
  {
    if (laz[k] == ei)
      return;
    laz[(k << 1) | 0] = h(laz[(k << 1) | 0], laz[k]);
    laz[(k << 1) | 1] = h(laz[(k << 1) | 1], laz[k]);
    dat[k] = reflect(k);
    laz[k] = ei;
  }

  inline void thrust(int k)
  {
    for (int i = height; i; i--)
      propagate(k >> i);
  }

  inline void recalc(int k)
  {
    while (k >>= 1)
      dat[k] = f(reflect((k << 1) | 0), reflect((k << 1) | 1));
  }

  void update(int a, int b, E x)
  {
    if (a >= b)
      return;
    thrust(a += n);
    thrust(b += n - 1);
    for (int l = a, r = b + 1; l < r; l >>= 1, r >>= 1)
    {
      if (l & 1)
        laz[l] = h(laz[l], x), l++;
      if (r & 1)
        --r, laz[r] = h(laz[r], x);
    }
    recalc(a);
    recalc(b);
  }

  void set_val(int a, T x)
  {
    thrust(a += n);
    dat[a] = x;
    laz[a] = ei;
    recalc(a);
  }

  T query(int a, int b)
  {
    if (a >= b)
      return ti;
    thrust(a += n);
    thrust(b += n - 1);
    T vl = ti, vr = ti;
    for (int l = a, r = b + 1; l < r; l >>= 1, r >>= 1)
    {
      if (l & 1)
        vl = f(vl, reflect(l++));
      if (r & 1)
        vr = f(reflect(--r), vr);
    }
    return f(vl, vr);
  }
};

int main()
{
  cin.tie(0);
  ios::sync_with_stdio(false);
  cout << setprecision(30) << setiosflags(ios::fixed);

  int n, q;
  cin >> n >> q;
  auto f = [](pll a, pll b) { return MP(a.first + b.first, a.second + b.second); };
  auto g = [](pll a, ll b) { return MP(a.second * b, a.second); };
  auto h = [](ll a, ll b) { return b; };
  SegmentTree<pll, ll> sg(f, g, h, MP(0, 0), -10000000);
  sg.build(vector<pll>(n, MP(0, 1)));
  rep(qi, q)
  {
    int type;
    cin >> type;
    if (type == 0)
    {
      ll s, t, x;
      cin >> s >> t >> x;
      sg.update(s, t + 1, x);
    }
    else if (type == 1)
    {
      ll s, t;
      cin >> s >> t;
      cout << sg.query(s, t + 1).first << "\n";
    }
  }

  return 0;
}