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;
int N,Q;
typedef long long ll;
const int INF=INT_MAX;
struct LazySegmentTree{
  private:
  int n;
  vector<int> node,lazy;
  vector<bool> lazyFlag;
  
  public:
  LazySegmentTree(vector<int> v){
    int sz=(int)v.size();
    n=1;  while(n<sz)n*=2;
    node.resize(2*n-1);
    lazy.resize(2*n-1,INF);
    lazyFlag.resize(2*n-1,false);
    for(int i=0;i<sz;i++)node[i+n-1]=v[i];
    for(int i=n-2;i>=0;i--){node[i]=node[2*i+1]+node[2*i+2];}
  }
  void lazyEvaluate(int k,int l,int r){
    if(lazyFlag[k]){
      node[k]=lazy[k]*(r-l);
      if(r-l>1){
        lazy[2*k+1]=lazy[2*k+2]=lazy[k];
        lazyFlag[2*k+1]=lazyFlag[2*k+2]=true;
      }
      lazyFlag[k]=false;
    }
  }
  void update(int a,int b,int x,int k=0,int l=0,int r=-1){
    if(r<0)r=n;
    lazyEvaluate(k,l,r);
    if(b<=l || r<=a)return;
    if(a<=l && r<=b){
      lazy[k]=x;
      lazyFlag[k]=true;
      lazyEvaluate(k,l,r);
    }
    else{
      update(a,b,x,2*k+1,l,(l+r)/2);
      update(a,b,x,2*k+2,(l+r)/2,r);
      node[k]=node[2*k+1]+node[2*k+2];
    }
  }
  ll getsum(int a,int b,int k=0,int l=0,int r=-1){
    if(r<0)r=n;
    lazyEvaluate(k,l,r);
    if(b<=l || r<=a)return 0;
    if(a<=l && r<=b)return node[k];
    ll vl=getsum(a,b,2*k+1,l,(l+r)/2);
    ll vr=getsum(a,b,2*k+2,(l+r)/2,r);
    return vl+vr;
  }
};

int main(){
  cin >> N >> Q;
  LazySegmentTree seg(vector<int>(N,0));
  for(int i=0;i<Q;i++){
    int q,s,t; cin >> q >> s >> t;
    if(q==0){
      int x; cin >> x;
      seg.update(s,t+1,x);
    }
    else{
      cout << seg.getsum(s,t+1) << endl;
    }
  }
}