Educational Codeforces Round 54 (Rated for Div. 2) ABCD

A. Minimizing the String

time limit per test

1 second

memory limit per test

256 megabytes

Description:

You are given a string ss consisting of nn lowercase Latin letters.

You have to remove at most one (i.e. zero or one) character of this string in such a way that the string you obtain will be lexicographically smallest among all strings that can be obtained using this operation.

String s=s1s2…sns=s1s2…sn is lexicographically smaller than string t=t1t2…tmt=t1t2…tm if n<mn<m and s1=t1,s2=t2,…,sn=tns1=t1,s2=t2,…,sn=tn or there exists a number pp such that p≤min(n,m)p≤min(n,m) and s1=t1,s2=t2,…,sp−1=tp−1s1=t1,s2=t2,…,sp−1=tp−1 and sp<tpsp<tp .

For example, "aaa" is smaller than "aaaa", "abb" is smaller than "abc", "pqr" is smaller than "z".

Input

The first line of the input contains one integer nn (2≤n≤2⋅1052≤n≤2⋅105 ) — the length of ss .

The second line of the input contains exactly nn lowercase Latin letters — the string ss .

Output

Print one string — the smallest possible lexicographically string that can be obtained by removing at most one character from the string ss .

Examples

Input

3 aaa

 

Output

aa

 

Input

5

abcda

 

Output

abca

 

Note

In the first example you can remove any character of ss to obtain the string "aa".

In the second example "abca" < "abcd" < "abcda" < "abda" < "acda" < "bcda".

题意：

在序列中至多删去一个数，使得操作后得序列最小（与执行相同操作的其它序列相比）

题解：

通过模拟一下这个过程可以发现我们要找 i 这个位置，满足si>si+1&&i<n 或者直接i=n。

代码如下：

#include <cstdio>
#include <cstring>
#include <algorithm>
#include <iostream>
using namespace std;
 
const int N = 2e5+;
char s[N];
int n;
 
int main(){
    scanf("%d",&n);getchar();
    for(int i=;i<=n;i++) scanf("%c",&s[i]);
    int i,pos=n;
    for(i=;i<n;i++){
        int j=i+;
        if(s[j]<s[i]){
            pos=i;
            break ;
        }
    }
    for(int i=;i<=n;i++){
        if(i==pos) continue ;
        printf("%c",s[i]);
    }
    return ;
} 

B. Divisor Subtraction

time limit per test

2 seconds

memory limit per test

256 megabytes

Description:

You are given an integer number nn. The following algorithm is applied to it:

1. if n=0, then end algorithm;
2. find the smallest prime divisor d of n;
3. subtract d from n and go to step 1.

Determine the number of subtrations the algorithm will make.

Input

The only line contains a single integer nn (2≤n≤10102≤n≤1010).

Output

Print a single integer — the number of subtractions the algorithm will make.

Examples

Input

5

Output

1

 

Input

4

Output

2

 

Note

In the first example 5 is the smallest prime divisor, thus it gets subtracted right away to make a 0.

In the second example 2 is the smallest prime divisor at both steps.

题意：

找n最小的质因子d，然后减去d，不断 重复这一过程直到n=0。

题解：

n为偶数很容易。当n为奇数时，质因子必为奇数，减去后也为偶数。所以问题的关键就是当n为奇数的情况。

最后发现只要找到一个最小的d，使得n%d==0就可以了，不管d是否为质数。

我当时没考虑到这一点，所以代码有点丑陋。

#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
#include <cmath>
using namespace std;
 
long long n;
 
inline int prim(int x){
    int flag = ;
    for(int i=;i<=sqrt(x+0.5)+;i++){
        if(x%i==){
            flag=;break ;
        }
    }
    return flag;
}
 
int main(){
    scanf("%lld",&n);
    if(n%==){
        printf("%lld",n/);return ;
    }
    if(prim(n)){
        printf("");return ;
    }
    for(int i=;i<=sqrt(n+0.5)+;i++){
        if(n%i== && prim(i)){
            printf("%lld",+(n-i)/);
            return ;
        }
    }
    return ;
} 

C. Meme Problem

time limit per test

1 second

memory limit per test

256 megabytes

Try guessing the statement from this picture:

You are given a non-negative integer dd . You have to find two non-negative real numbers aa and bb such that a+b=d and a⋅b=d .

Input

The first line contains tt (1≤t≤1031≤t≤103 ) — the number of test cases.

Each test case contains one integer d (0≤d≤103) .

Output

For each test print one line.

If there is an answer for the i -th test, print "Y", and then the numbers a and b .

If there is no answer for the i -th test, print "N".

Your answer will be considered correct if |(a+b)−a⋅b|≤10−6|(a+b)−a⋅b|≤10−6 and |(a+b)−d|≤10−6|(a+b)−d|≤10−6 .

 

Example

Input

7
69
0
1
4
5
999
1000

Output

Y 67.985071301 1.014928699
Y 0.000000000 0.000000000
N
Y 2.000000000 2.000000000
Y 3.618033989 1.381966011
Y 997.998996990 1.001003010
Y 998.998997995 1.00100200

题意：

给出一个数d，找两个数x,y，满足x+y=d 并且x*y=d。

 

题解：

我用的是二分，当时好像证明了二分的正确性。但实际上有更简单的数学方法，就是利用x+y=d,x*y=d这两个等式（韦达定理），变换一下可以解一个方程。

 

我还是给出我的二分代码吧。。

#include <cstdio>
#include <cstring>
#include <algorithm>
#include <iostream>
#include <cmath>
using namespace std;
 
int t,n;
double eps = 1e-;
 
int main(){
    scanf("%d",&t);
    while(t--){
        scanf("%d",&n);
        if(n==){
            printf("Y 0.000000000 0.000000000\n");
            continue ;
        }else if(n== || n== ||n==){
            printf("N\n");continue;
        }else if(n==){
            printf("Y 2.000000000 2.000000000\n");
            continue ;
        }else{
            double l = ,r=,mid,Ans,tmp;
            while(l<=r){
                mid=(l+r)/;
                tmp = n-mid;
                if(abs(tmp*mid-tmp-mid)<eps || abs(tmp*mid-n)<eps){
                    Ans=mid;break;
                }
                if(tmp*mid-tmp-mid<) l=mid+0.0000000001;
                else r=mid-0.0000000001;
            }
            printf("Y %.9lf %.9lf\n",n-Ans,Ans);
        }
    }
 
    return ;
} 

D. Edge Deletion

time limit per test

2.5 seconds

memory limit per test

256 megabytes

Description:

You are given an undirected connected weighted graph consisting of nn vertices and mm edges. Let's denote the length of the shortest path from vertex 11 to vertex ii as didi .

You have to erase some edges of the graph so that at most kk edges remain. Let's call a vertex ii good if there still exists a path from 11 to ii with length didi after erasing the edges.

Your goal is to erase the edges in such a way that the number of good vertices is maximized.

Input

The first line contains three integers nn , mm and kk (2≤n≤3⋅1052≤n≤3⋅105 , 1≤m≤3⋅1051≤m≤3⋅105 , n−1≤mn−1≤m , 0≤k≤m0≤k≤m ) — the number of vertices and edges in the graph, and the maximum number of edges that can be retained in the graph, respectively.

Then mm lines follow, each containing three integers xx , yy , ww (1≤x,y≤n1≤x,y≤n , x≠yx≠y , 1≤w≤1091≤w≤109 ), denoting an edge connecting vertices xx and yy and having weight ww .

The given graph is connected (any vertex can be reached from any other vertex) and simple (there are no self-loops, and for each unordered pair of vertices there exists at most one edge connecting these vertices).

Output

In the first line print ee — the number of edges that should remain in the graph (0≤e≤k0≤e≤k ).

In the second line print ee distinct integers from 11 to mm — the indices of edges that should remain in the graph. Edges are numbered in the same order they are given in the input. The number of good vertices should be as large as possible.

Examples

Input

3 3 2

1 2 1

3 2 1

1 3 3

Output

2

1 2

 

Input

4 5 2

4 1 8

2 4 1

2 1 3

3 4 9

3 1 5

Output

2

3 2

 

题意：

这个复制粘贴过来好像有点问题...将就看吧。

题目的要求就是可以留下最多k条边，使得最后的图中所有的点的最小距离都跟未删边一样。

 

题解：

题解还是好像，但是代码实现起来坑了我好久...

这题spfa会被卡，所以用了dijsktra。

我们可以发现，最短的最短路径树就是答案，然后记录结果的时候就当点从优先队列里面取出来的时候记录就可以了，因为Dijsktra中，点取出来的时候就是当前最小距离。

 

代码如下：

#include <cstdio>
#include <cstring>
#include <algorithm>
#include <iostream>
#include <queue>
#include <vector>
#define INF 1e18
using namespace std;
 
typedef long long LL;
typedef pair<LL,int> pli;
typedef pair<int,int> pii;
 
const int N = 3e5+;
int n,m,k;
int vis[N]={};
LL d[N];
pli pre[N];
vector<pair<int,pii> > vec[N];
vector<int> ans ;
void Dij(int x){
    fill(d,d+n+,INF);d[x]=0ll;
    priority_queue<pli,vector<pli>,greater<pli> > q;
    q.push(make_pair(d[x],x));
    while(!q.empty()){
        pli now = q.top();q.pop();
        int u = now.second;
        if(vis[u]) continue ;
        vis[u]=;
        for(int i=;i<vec[u].size();i++){
            int v = vec[u][i].second.first;
            if(d[v]>d[u]+vec[u][i].second.second &&!vis[v]){
                d[v]=d[u]+vec[u][i].second.second;
                pre[v]=make_pair(u,vec[u][i].first);
                q.push(make_pair(d[v],v));
            }
        }
    }
}
queue <int> que ;
void bfs(int x,int K){
    que.push(x);
    while(!que.empty() && K){
        int u = que.front();que.pop();
        for(int i=;i<vec[u].size();i++){
            int v = vec[u][i].second.first ;
            if(d[v]==d[u]+vec[u][i].second.second){
                que.push(v);
                ans.push_back(vec[u][i].first);
                K--;
            }
            if(!K) break ;
        }
    }
}
int main(){
    scanf("%d%d%d",&n,&m,&k);
    for(int i=,u,v,c;i<=m;i++){
        scanf("%d%d%d",&u,&v,&c);
        vec[u].push_back(make_pair(i,make_pair(v,c)));
        vec[v].push_back(make_pair(i,make_pair(u,c)));
    }
    Dij();
    bfs(,k);
    printf("%d\n",ans.size());
    for(int i=;i<ans.size();i++) printf("%d ",ans[i]);
    return ;
}