A. Splits

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

Let's define a split of n as a nonincreasing sequence of positive integers, the sum of which is n.

For example, the following sequences are splits of 8: [4, 4], [3, 3, 2], [2, 2, 1, 1, 1, 1], [5, 2, 1].

The following sequences aren't splits of 8: [1, 7], [5, 4], [11,  - 3], [1, 1, 4, 1, 1].

The weight of a split is the number of elements in the split that are equal to the first element. For example, the weight of the split [1, 1, 1, 1, 1] is 5, the weight of the split [5, 5, 3, 3, 3] is 2 and the weight of the split [9] equals 1.

For a given n, find out the number of different weights of its splits.

Input

The first line contains one integer n (1 ≤ n ≤ 109).

Output

Output one integer — the answer to the problem.

Examples

input

Copy

7

output

Copy

4

input

Copy

8

output

Copy

5

input

Copy

9

output

Copy

5

Note

In the first sample, there are following possible weights of splits of 7:

Weight 1: []

Weight 2: [, , 1]

Weight 3: [, , , 1]

Weight 7: [, , , , , , ]

把一个数分为不同的集合(元素可以重复)，和为n

n是奇数，长度为n的，n/2+1，。。。1（长度为2不存在）

n是偶数，长度为n，长度为n/2。。。1（均可以存在）

所以结论就是n/2+1

#include 
      
       using namespace std;typedef long long ll;int main(){    int n;    cin>>n;    cout<
      

B. Messages

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

There are n incoming messages for Vasya. The i-th message is going to be received after ti minutes. Each message has a cost, which equals to A initially. After being received, the cost of a message decreases by B each minute (it can become negative). Vasya can read any message after receiving it at any moment of time. After reading the message, Vasya's bank account receives the current cost of this message. Initially, Vasya's bank account is at 0.

Also, each minute Vasya's bank account receives C·k, where k is the amount of received but unread messages.

Vasya's messages are very important to him, and because of that he wants to have all messages read after T minutes.

Determine the maximum amount of money Vasya's bank account can hold after T minutes.

Input

The first line contains five integers n, A, B, C and T (1 ≤ n, A, B, C, T ≤ 1000).

The second string contains n integers ti (1 ≤ ti ≤ T).

Output

Output one integer  — the answer to the problem.

Examples

input

Copy

4 5 5 3 5 1 5 5 4

output

Copy

20

input

Copy

5 3 1 1 3 2 2 2 1 1

output

Copy

15

input

Copy

5 5 3 4 5 1 2 3 4 5

output

Copy

35

Note

In the first sample the messages must be read immediately after receiving, Vasya receives A points for each message, n·A = 20 in total.

In the second sample the messages can be read at any integer moment.

In the third sample messages must be read at the moment T. This way Vasya has 1, 2, 3, 4 and 0 unread messages at the corresponding minutes, he gets 40 points for them. When reading messages, he receives (5 - 4·3) + (5 - 3·3) + (5 - 2·3) + (5 - 1·3) + 5 =  - 5 points. This is 35 in total.

昨天晚上没有这个Note啊，毒瘤

所以就是看下(T-t[i])*(c-b)的正负啊，%%%聚聚

#include 
       
        using namespace std;typedef long long ll;long long ans;int t[1005];int main(){    int n,a,b,c,T;    cin>>n>>a>>b>>c>>T;    for(int i=1;i<=n;i++)        cin>>t[i];    for(int i=1;i<=n;i++)       if((T-t[i])*(c-b)<=0)          ans+=a;       else          ans+=a+(T-t[i])*(c-b);    cout<
       

C. Alternating Sum

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

You are given two integers $\mathrm{aa and bb.\; Moreover,\; you\; are\; given\; a\; sequence s0,s1,\dots ,sns0,s1,\dots ,sn.\; All\; values\; in ss are\; integers 11 or -1-1.\; It\text{'}s\; known\; that\; sequence\; is kk-periodic\; and kk divides n+1n+1.\; In\; other\; words,\; for\; each k\le i\le nk\le i\le n it\text{'}s\; satisfied\; that si=si-ksi=si-k.}$

Find out the non-negative remainder of division of $\stackrel{}{}$

Note that the modulo is unusual!

Input

The first line contains four integers $\mathrm{n,a,bn,a,b and kk (1\le n\le 109,1\le a,b\le 109,1\le k\le 105)(1\le n\le 109,1\le a,b\le 109,1\le k\le 105).}$

The second line contains a sequence of length $\mathrm{kk consisting\; of\; characters\; \text{'}+\text{'}\; and\; \text{'}-\text{'}.}$

If the $\mathrm{ii-th\; character\; (0-indexed)\; is\; \text{'}+\text{'},\; then si=1si=1,\; otherwise si=-1si=-1.}$

Note that only the first $\mathrm{kk members\; of\; the\; sequence\; are\; given,\; the\; rest\; can\; be\; obtained\; using\; the\; periodicity\; property.}$

Output

Output a single integer — value of given expression modulo ${\mathrm{109+9109+9.}}^{}$

Examples

input

Copy

2 2 3 3 +-+

output

Copy

7

input

Copy

4 1 5 1 -

output

Copy

999999228

Note

In the first example:

$(n\sum i=0sian-ibi)(\sum i=0nsian-ibi) = 2230-2131+20322230-2131+2032 =\; 7$

In the second example:

$(n\sum i=0sian-ibi)=-1450-1351-1252-1153-1054=-781\equiv 999999228(mod109+9)(\sum i=0nsian-ibi)=-1450-1351-1252-1153-1054=-781\equiv 999999228(mod109+9).$

#include 
        
         using namespace std;typedef long long ll;const ll MD=1e9+9;ll po(ll a,ll b){    ll ans=1;    while(b)    {        if(b&1)ans=ans*a%MD;        b>>=1,a=a*a%MD;    }    return ans;}int main(){    ll n,a,b,k;    cin>>n>>a>>b>>k;    string s;    cin>>s;    ll cur=0;    for(int i=0;i