CodeForces - 444C

F - DZY Loves Colors

DZY loves colors, and he enjoys painting.

On a colorful day, DZY gets a colorful ribbon, which consists of n units (they are numbered from 1 to n from left to right). The color of the i-th unit of the ribbon is i at first. It is colorful enough, but we still consider that the colorfulness of each unit is 0 at first.

DZY loves painting, we know. He takes up a paintbrush with color x and uses it to draw a line on the ribbon. In such a case some contiguous units are painted. Imagine that the color of unit i currently is y. When it is painted by this paintbrush, the color of the unit becomes x, and the colorfulness of the unit increases by |x - y|.

DZY wants to perform m operations, each operation can be one of the following:

1. Paint all the units with numbers between l and r (both inclusive) with color x.
2. Ask the sum of colorfulness of the units between l and r (both inclusive).

Can you help DZY?

Input

The first line contains two space-separated integers n, m (1 ≤ n, m ≤ 10⁵).

Each of the next m lines begins with a integer type (1 ≤ type ≤ 2), which represents the type of this operation.

If type = 1, there will be 3 more integers l, r, x (1 ≤ l ≤ r ≤ n; 1 ≤ x ≤ 10⁸) in this line, describing an operation 1.

If type = 2, there will be 2 more integers l, r (1 ≤ l ≤ r ≤ n) in this line, describing an operation 2.

Output

For each operation 2, print a line containing the answer — sum of colorfulness.

Examples

Input

3 3
1 1 2 4
1 2 3 5
2 1 3

Output

8

Input

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

Output

3
2
1

Input

10 6
1 1 5 3
1 2 7 9
1 10 10 11
1 3 8 12
1 1 10 3
2 1 10

Output

129

Note

In the first sample, the color of each unit is initially [1, 2, 3], and the colorfulness is [0, 0, 0].

After the first operation, colors become [4, 4, 3], colorfulness become [3, 2, 0].

After the second operation, colors become [4, 5, 5], colorfulness become [3, 3, 2].

So the answer to the only operation of type 2 is 8.

 #include <cstdio>
 #include <stack>
 #include <cmath>
 #include <queue>
 #include <string>
 #include <queue>
 #include <cstring>
 #include <iostream>
 #include <algorithm>

 #define lid id<<1
 #define rid id<<1|1
 #define closein cin.tie(0)
 #define scac(a) scanf("%c",&a)
 #define scad(a) scanf("%d",&a)
 //#define print(a) printf("%d\n",a)
 #define debug printf("hello world")
 #define form(i,n,m) for(int i=n;i<m;i++)
 #define mfor(i,n,m) for(int i=n;i>m;i--)
 #define nfor(i,n,m) for(int i=n;i>=m;i--)
 #define forn(i,n,m) for(int i=n;i<=m;i++)
 #define scadd(a,b) scanf("%d%d",&a,&b)
 #define memset0(a) memset(a,0,sizeof(a))
 #define scaddd(a,b,c) scanf("%d%d%d",&a,&b,&c)
 #define scadddd(a,b,c,d) scanf("%d%d%d%d",&a,&b,&c,&d)

 #define INF 0x3f3f3f3f
 #define maxn 100005
 typedef long long ll;
 using namespace std;
 //---------AC(^-^)AC---------\\

 int n,m,block,num;
 int blo[maxn],l[maxn],r[maxn];
 ll color[maxn],sum[maxn],allsum[maxn],flag2[maxn],flag[maxn];

 void print()
 {
     forn(i,,num)
     {
         printf("%lld %lld\n",allsum[i],flag2[i]);
     }
     debug;
     printf("\n");
     forn(i,,n)
         printf("%lld %lld\n",color[i],sum[i]);
 }
 void push_down(int id)
 {
     forn(i,l[id],r[id]) color[i]=flag[id];
     flag[id]=-;
 }
 void update(int ld,int rd,int add)
 {
     if(blo[ld]==blo[rd])
     {
         if(flag[blo[ld]]!=-)    push_down(blo[ld]);
         forn(i,ld,rd)    {
             sum[i]+=abs(color[i]-add);
             allsum[blo[ld]]+=abs(color[i]-add);
             color[i]=add;
         }
     }else {
         if(flag[blo[ld]]!=-) push_down(blo[ld]);
         forn(i,ld,r[blo[ld]]) {
             sum[i]+=abs(color[i]-add);
             allsum[blo[ld]]+=abs(color[i]-add);
             color[i]=add;
         }
         forn(i,blo[ld]+,blo[rd]-)    {
             if(flag[i]!=-)    {
                 allsum[i]+=abs(flag[i]-add)*(r[i]-l[i]+);
                 flag2[i]+=abs(flag[i]-add);
                 flag[i]=add;
             }else {
                 forn(j,l[i],r[i])    {
                     sum[j]+=abs(color[j]-add);
                     allsum[i]+=abs(color[j]-add);
                     color[j]=add;
                 }
                 flag[i]=add;
             }
         }
         if(flag[blo[rd]]!=-) push_down(blo[rd]);
         forn(i,l[blo[rd]],rd)    {
             sum[i]+=abs(color[i]-add);
             allsum[blo[rd]]+=abs(color[i]-add);
             color[i]=add;
         }
     }
     //print();
 }
 void query(int ld,int rd)
 {
     ll ans=;
     if(blo[ld]==blo[rd])    {
         forn(i,ld,rd) ans+=sum[i]+flag2[blo[i]];
     }else {
         forn(i,ld,r[blo[ld]])    {
             ans+=sum[i]+flag2[blo[i]];
         }
         forn(i,blo[ld]+,blo[rd]-)    {
             ans+=allsum[i];
         }
         forn(i,l[blo[rd]],rd)    {
             ans+=sum[i]+flag2[blo[i]];
         }
     }
     printf("%lld\n",ans);
 }

 int main()
 {
     scadd(n,m);
     block=sqrt(n);
     num=(n-)/block+;
     forn(i,,n)    {
         color[i]=i;
         blo[i]=(i-)/block+;
     }
     forn(i,,num) {
         l[i]=(i-)*block+;
         r[i]=i*block;
     }
     r[num]=n;
     forn(i,,num) flag[i]=-;
     while(m--)
     {
         int op,l,r;
         scaddd(op,l,r);
         if(op==)
         {
             int x;
             scad(x);
             update(l,r,x);
         }
         else
         {
             query(l,r);
             //print();
         }
     }
     return ;
 }