//CLOCKS_PER_SEC
using namespace std;
#include<bits/stdc++.h>
#define sqr(x) 1ll*(x)*(x)
//#define sort stable_sort
#define ll long long
#define mk make_pair
#define pb push_back
#define in insert
#define mtr(x,y,z) mk(mk(x,y),z)
#define fi first
#define se second
#define lch(x) ((x)<<1)
#define rch(x) (((x)<<1)|1)
#define all(x) (x).begin(),(x).end()
#define titose CLOCKS_PER_SEC
#define fpi(x) freopen(x,"r",stdin);
#define fpo(x) freopen(x,"w",stdout);
#define fprio fpi("in.txt");fpo("out.txt");
#define fast ios_base::sync_with_stdio(false);
inline void read(int &x){int v=0,f=1;char c=getchar();while (!isdigit(c)&&c!='-') c=getchar();if (c=='-') f=-1; else v=(c&15);while (isdigit(c=getchar())) v=(v<<1)+(v<<3)+(c&15);x=v*f;}
inline void read(ll &x){ll v=0ll,f=1ll;char c=getchar();while (!isdigit(c)&&c!='-') c=getchar();if (c=='-') f=-1; else v=(c&15);while (isdigit(c=getchar())) v=(v<<1)+(v<<3)+(c&15);x=v*f;}
inline void readc(char &x){char c;while (((c=getchar())==' ')||c=='\n');x=c;}
#define pii pair<int,int>
#define pll pair<ll,ll>
#define vl vector<ll>
#define si set<int>
//#define sl set<ll>
#define mii map<int,int>
#define mll map<ll,ll>
#define msi map<string,int>
#define msl map<string,ll>
#define piii pair<int,pii >
#define piipi pair<pii,int>
#define plll pair<ll,pll >
#define pllpl pair<pll,ll>
#define pqi priority_queue<int>
#define pql priority_queue<ll>
#define npqi priority_queue<int,vector<int>,greater<int> >
#define npql priority_queue<ll,vector<ll>,greater<ll> >
#define forup(i,a,b) for ((i)=(a);(i)<=(b);(i)++)
#define fordo(i,a,b) for ((i)=(a);(i)>=(b);(i)--)
#define rep(i,x) forup ((i),1,(x))
#define repd(i,x) fordo ((i),(x),1)
#define rep0(i,x) forup ((i),0,((int)(x))-1)
#define rep0d(i,x) fordo ((i),((int)(x))-1,0)
#define itr iterator
#define fe(itcalc,c) for(__typeof((c).begin()) itcalc=(c).begin();itcalc!=(c).end();itcalc++)
#define NO {cout<<"NO";return 0;}
#define YES {cout<<"YES";return 0;}
#define y0 y000000000000000000000000000
#define y1 y111111111111111111111111111
#define j0 j000000000000000000000000000
#define j1 j111111111111111111111111111
#define cl0(a) memset((a),(0),(sizeof((a))))
#define clz(a) memset((a),(0x16),(sizeof((a))))
#define clf(a) memset((a),(-(0x16)),(sizeof((a))))
#define inf 0x3bbbbbbb
#define lnf 0x2bbbbbbbbbbbbbbbll
//#define sqrt divi
#define p2(i) (1ll<<(i))
#define readi read
#define readll read
/*************************************************/
int n,m,i,j,l1[100005],r1[100005],l2[100005],r2[100005],fl[100005],fr[100005],gl[100005],gr[100005],v[100005];
int main()
{
	read(n);read(m);
	rep(i,n){
		read(v[i]);
		read(l1[i]);read(r1[i]);
		read(l2[i]);read(r2[i]);
	}
	fl[n+1]=0;fr[n+1]=m;
	gl[n+1]=0;gr[n+1]=m;
	repd(i,n){
		if(l1[i]<=v[i]&&v[i]<=r1[i]){
			fl[i]=l2[i];fr[i]=r2[i];
			if(!(gl[i+1]<=v[i]&&v[i]<=gr[i+1])){
				fl[i]=max(fl[i],fl[i+1]);
				fr[i]=min(fr[i],fr[i+1]);
			}
		}
		else{
			fl[i]=m;fr[i]=0;
		}
		if(l2[i]<=v[i]&&v[i]<=r2[i]){
			gl[i]=l1[i];gr[i]=r1[i];
			if(!(fl[i+1]<=v[i]&&v[i]<=fr[i+1])){
				gl[i]=max(gl[i],gl[i+1]);
				gr[i]=min(gr[i],gr[i+1]);
			}
		}
		else{
			gl[i]=m;gr[i]=0;
		}
	}
	if(fl[1]>0&&gl[1]>0){
		puts("No");
		return 0;
	}
	puts("Yes");
	int x=0,y=0;
	rep(i,n){
		if(fl[i]<=y&&y<=fr[i]){
			x=v[i];
			printf("0 ");
		}
		else{
			y=v[i];
			printf("1 ");
		}
	}
	return 0;
}
### Prompt

In Cpp, your task is to solve the following problem:

The Alice's computer is broken, so she can't play her favorite card game now. To help Alice, Bob wants to answer n her questions. 

Initially, Bob holds one card with number 0 in the left hand and one in the right hand. In the i-th question, Alice asks Bob to replace a card in the left or right hand with a card with number k_i (Bob chooses which of two cards he changes, Bob must replace exactly one card).

After this action, Alice wants the numbers on the left and right cards to belong to given segments (segments for left and right cards can be different). Formally, let the number on the left card be x, and on the right card be y. Then after the i-th swap the following conditions must be satisfied: a_{l, i} ≤ x ≤ b_{l, i}, and a_{r, i} ≤ y ≤ b_{r,i}.

Please determine if Bob can answer all requests. If it is possible, find a way to do it.

Input

The first line contains two integers n and m (2 ≤ n ≤ 100 000, 2 ≤ m ≤ 10^9) — the number of questions and the maximum possible value on the card.

Then n queries are described. Every description contains 3 lines.

The first line of the description of the i-th query contains a single integer k_i (0 ≤ k_i ≤ m) — the number on a new card.

The second line of the description of the i-th query contains two integers a_{l, i} and b_{l, i} (0 ≤ a_{l, i} ≤ b_{l, i} ≤ m) — the minimum and maximum values of the card at the left hand after the replacement.

The third line of the description of the i-th query contains two integers a_{r, i} and b_{r,i} (0 ≤ a_{r, i} ≤ b_{r,i} ≤ m) — the minimum and maximum values of the card at the right hand after the replacement.

Output

At the first line, print "Yes", if Bob can answer all queries, and "No" otherwise.

If Bob can answer all n queries, then at the second line print n numbers: a way to satisfy all requirements. If in i-th query Bob needs to replace the card in the left hand, print 0, otherwise print 1. If there are multiple answers, print any.

Examples

Input


2 10
3
0 3
0 2
2
0 4
0 2


Output


Yes
0 1 

Input


2 10
3
0 3
0 2
2
3 4
0 1


Output


No

Input


5 10
3
0 3
0 3
7
4 7
1 3
2
2 3
3 7
8
1 8
1 8
6
1 6
7 10


Output


Yes
1 0 0 1 0 

### Response

```cpp
//CLOCKS_PER_SEC
using namespace std;
#include<bits/stdc++.h>
#define sqr(x) 1ll*(x)*(x)
//#define sort stable_sort
#define ll long long
#define mk make_pair
#define pb push_back
#define in insert
#define mtr(x,y,z) mk(mk(x,y),z)
#define fi first
#define se second
#define lch(x) ((x)<<1)
#define rch(x) (((x)<<1)|1)
#define all(x) (x).begin(),(x).end()
#define titose CLOCKS_PER_SEC
#define fpi(x) freopen(x,"r",stdin);
#define fpo(x) freopen(x,"w",stdout);
#define fprio fpi("in.txt");fpo("out.txt");
#define fast ios_base::sync_with_stdio(false);
inline void read(int &x){int v=0,f=1;char c=getchar();while (!isdigit(c)&&c!='-') c=getchar();if (c=='-') f=-1; else v=(c&15);while (isdigit(c=getchar())) v=(v<<1)+(v<<3)+(c&15);x=v*f;}
inline void read(ll &x){ll v=0ll,f=1ll;char c=getchar();while (!isdigit(c)&&c!='-') c=getchar();if (c=='-') f=-1; else v=(c&15);while (isdigit(c=getchar())) v=(v<<1)+(v<<3)+(c&15);x=v*f;}
inline void readc(char &x){char c;while (((c=getchar())==' ')||c=='\n');x=c;}
#define pii pair<int,int>
#define pll pair<ll,ll>
#define vl vector<ll>
#define si set<int>
//#define sl set<ll>
#define mii map<int,int>
#define mll map<ll,ll>
#define msi map<string,int>
#define msl map<string,ll>
#define piii pair<int,pii >
#define piipi pair<pii,int>
#define plll pair<ll,pll >
#define pllpl pair<pll,ll>
#define pqi priority_queue<int>
#define pql priority_queue<ll>
#define npqi priority_queue<int,vector<int>,greater<int> >
#define npql priority_queue<ll,vector<ll>,greater<ll> >
#define forup(i,a,b) for ((i)=(a);(i)<=(b);(i)++)
#define fordo(i,a,b) for ((i)=(a);(i)>=(b);(i)--)
#define rep(i,x) forup ((i),1,(x))
#define repd(i,x) fordo ((i),(x),1)
#define rep0(i,x) forup ((i),0,((int)(x))-1)
#define rep0d(i,x) fordo ((i),((int)(x))-1,0)
#define itr iterator
#define fe(itcalc,c) for(__typeof((c).begin()) itcalc=(c).begin();itcalc!=(c).end();itcalc++)
#define NO {cout<<"NO";return 0;}
#define YES {cout<<"YES";return 0;}
#define y0 y000000000000000000000000000
#define y1 y111111111111111111111111111
#define j0 j000000000000000000000000000
#define j1 j111111111111111111111111111
#define cl0(a) memset((a),(0),(sizeof((a))))
#define clz(a) memset((a),(0x16),(sizeof((a))))
#define clf(a) memset((a),(-(0x16)),(sizeof((a))))
#define inf 0x3bbbbbbb
#define lnf 0x2bbbbbbbbbbbbbbbll
//#define sqrt divi
#define p2(i) (1ll<<(i))
#define readi read
#define readll read
/*************************************************/
int n,m,i,j,l1[100005],r1[100005],l2[100005],r2[100005],fl[100005],fr[100005],gl[100005],gr[100005],v[100005];
int main()
{
	read(n);read(m);
	rep(i,n){
		read(v[i]);
		read(l1[i]);read(r1[i]);
		read(l2[i]);read(r2[i]);
	}
	fl[n+1]=0;fr[n+1]=m;
	gl[n+1]=0;gr[n+1]=m;
	repd(i,n){
		if(l1[i]<=v[i]&&v[i]<=r1[i]){
			fl[i]=l2[i];fr[i]=r2[i];
			if(!(gl[i+1]<=v[i]&&v[i]<=gr[i+1])){
				fl[i]=max(fl[i],fl[i+1]);
				fr[i]=min(fr[i],fr[i+1]);
			}
		}
		else{
			fl[i]=m;fr[i]=0;
		}
		if(l2[i]<=v[i]&&v[i]<=r2[i]){
			gl[i]=l1[i];gr[i]=r1[i];
			if(!(fl[i+1]<=v[i]&&v[i]<=fr[i+1])){
				gl[i]=max(gl[i],gl[i+1]);
				gr[i]=min(gr[i],gr[i+1]);
			}
		}
		else{
			gl[i]=m;gr[i]=0;
		}
	}
	if(fl[1]>0&&gl[1]>0){
		puts("No");
		return 0;
	}
	puts("Yes");
	int x=0,y=0;
	rep(i,n){
		if(fl[i]<=y&&y<=fr[i]){
			x=v[i];
			printf("0 ");
		}
		else{
			y=v[i];
			printf("1 ");
		}
	}
	return 0;
}
```