C. Coffee Break

Recently Monocarp got a job. His working day lasts exactly mm minutes. During work, Monocarp wants to drink coffee at certain moments: there are nn minutes a1,a2,…,ana1,a2,…,an, when he is able and willing to take a coffee break (for the sake of simplicity let's consider that each coffee break lasts exactly one minute).

However, Monocarp's boss doesn't like when Monocarp takes his coffee breaks too often. So for the given coffee break that is going to be on minute aiai, Monocarp must choose the day in which he will drink coffee during the said minute, so that every day at least dd minutes pass between any two coffee breaks. Monocarp also wants to take these nn coffee breaks in a minimum possible number of working days (he doesn't count days when he is not at work, and he doesn't take coffee breaks on such days). Take into account that more than dd minutes pass between the end of any working day and the start of the following working day.

For each of the nn given minutes determine the day, during which Monocarp should take a coffee break in this minute. You have to minimize the number of days spent.

Input

The first line contains three integers nn, mm, dd (1≤n≤2⋅105,n≤m≤109,1≤d≤m)(1≤n≤2⋅105,n≤m≤109,1≤d≤m) — the number of coffee breaks Monocarp wants to have, the length of each working day, and the minimum number of minutes between any two consecutive coffee breaks.

The second line contains nn distinct integers a1,a2,…,ana1,a2,…,an (1≤ai≤m)(1≤ai≤m), where aiai is some minute when Monocarp wants to have a coffee break.

Output

In the first line, write the minimum number of days required to make a coffee break in each of the nn given minutes.

In the second line, print nn space separated integers. The ii-th of integers should be the index of the day during which Monocarp should have a coffee break at minute aiai. Days are numbered from 11. If there are multiple optimal solutions, you may print any of them.

Examples

input

Copy

4 5 3
3 5 1 2

output

Copy

3
3 1 1 2 

input

Copy

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

output

Copy

2
2 1 1 2 2 1 2 1 1 2 

題意：給你n個數，選出一些作為一組，要求一組中相鄰兩數間隔至少為d，問你最少能分幾組，並輸出每個數字在第幾組？

思路：把這些數扔到set裡，每次選第一個數，接下來用upper_bound掃描即可，如果有間隔為大於d的，記錄該數在第幾組，同時erase它，保證每個數字只掃描一次，刪除一次，複雜度大概O（n*logn*logn）。

#include <bits/stdc++.h>
#define ll long long
using namespace std;
map<int,int>mp;
set<int>st;
set<int>::iterator it,it1,it2;
int n,m,d,a[200020];
int main()
{
    while(~scanf("%d%d%d",&n,&m,&d))
    {
        st.clear();
        mp.clear();
        for(int i=1;i<=n;i++)
        {
            scanf("%d",&a[i]);
            st.insert(a[i]);
        }
        int ans=0;
        for(it=st.begin();it!=st.end();it++)   //迭代所有元素
        {
            ans++;
            it1=it;
            mp[*it1]=ans;
            while(1)
            {
                it2=st.upper_bound((*it1)+d);
                if(it2==st.end())break;   //找不到就終止
                else
                {
                    mp[(*it2)]=ans;
                    it1=it2;
                    st.erase(it2);
                }
            }
        }
        printf("%d\n",ans);
        for(int i=1;i<=n;i++)printf("%d ",mp[a[i]]);
        printf("\n");
    }
}