Educational Codeforces Round 15 A， B ， C 暴力 ， map ， 二分

A. Maximum Increase

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

You are given array consisting of n integers. Your task is to find the maximum length of an increasing subarray of the given array.

A subarray is the sequence of consecutive elements of the array. Subarray is called increasing if each element of this subarray strictly greater than previous.

Input

The first line contains single positive integer n (1 ≤ n ≤ 10⁵) — the number of integers.

The second line contains n positive integers a₁, a₂, ..., a_n (1 ≤ a_i ≤ 10⁹).

Output

Print the maximum length of an increasing subarray of the given array.

Examples

Input

5
1 7 2 11 15

Output

3

Input

6
100 100 100 100 100 100

Output

1

Input

3
1 2 3

Output

3
题意：找到连续的上升子序列；
思路：暴力就行；

#include<bits/stdc++.h>
using namespace std;
#define ll __int64
#define esp 0.00000000001
const int N=3e3+10,M=1e6+10,inf=1e9+10,mod=1000000007;
int a[M];
int main()
{
    int x,y,z,i,t;
    scanf("%d",&x);
    int ans=0,sum=0,pre=0;
    for(i=1;i<=x;i++)
    {
        scanf("%d",&y);
        if(y>pre)
        sum++;
        else
        sum=1;
        pre=y;
        ans=max(ans,sum);
    }
    printf("%d
",ans);
    return 0;
}

B. Powers of Two

time limit per test

3 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

You are given n integers a₁, a₂, ..., a_n. Find the number of pairs of indexes i, j (i < j) that a_i + a_j is a power of 2 (i. e. some integer x exists so that a_i + a_j = 2^x).

Input

The first line contains the single positive integer n (1 ≤ n ≤ 10⁵) — the number of integers.

The second line contains n positive integers a₁, a₂, ..., a_n (1 ≤ a_i ≤ 10⁹).

Output

Print the number of pairs of indexes i, j (i < j) that a_i + a_j is a power of 2.

Examples

Input

4
7 3 2 1

Output

2

Input

3
1 1 1

Output

3

Note

In the first example the following pairs of indexes include in answer: (1, 4) and (2, 4).

In the second example all pairs of indexes (i, j) (where i < j) include in answer.

题意：n个数，选两个相加求为2的阶乘的个数；

思路：两个数相加最大为2e9，一共30个数；枚举二的阶乘；

　　　复杂度N*30；

#include<bits/stdc++.h>
using namespace std;
#define ll __int64
#define esp 0.00000000001
const int N=3e3+10,M=1e6+10,inf=1e9+10,mod=1000000007;
int er[50];
int a[M];
map<int,int>m;
int main()
{
    int x,y,z,i,t;
    for(i=1;i<=30;i++)
    er[i]=(1<<i);
    scanf("%d",&x);
    for(i=1;i<=x;i++)
    scanf("%d",&a[i]),m[a[i]]++;
    ll ans=0;
    for(i=1;i<=x;i++)
    {
        for(t=1;t<=30;t++)
        {
            int v=er[t]-a[i];
            if(v==a[i])
            ans+=m[v]-1;
            else
            ans+=m[v];
        }
    }
    printf("%I64d
",ans/2);
    return 0;
}

C. Cellular Network

time limit per test

3 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

You are given n points on the straight line — the positions (x-coordinates) of the cities and m points on the same line — the positions (x-coordinates) of the cellular towers. All towers work in the same way — they provide cellular network for all cities, which are located at the distance which is no more than r from this tower.

Your task is to find minimal r that each city has been provided by cellular network, i.e. for each city there is at least one cellular tower at the distance which is no more than r.

If r = 0 then a tower provides cellular network only for the point where it is located. One tower can provide cellular network for any number of cities, but all these cities must be at the distance which is no more than r from this tower.

Input

The first line contains two positive integers n and m (1 ≤ n, m ≤ 10⁵) — the number of cities and the number of cellular towers.

The second line contains a sequence of n integers a₁, a₂, ..., a_n ( - 10⁹ ≤ a_i ≤ 10⁹) — the coordinates of cities. It is allowed that there are any number of cities in the same point. All coordinates a_i are given in non-decreasing order.

The third line contains a sequence of m integers b₁, b₂, ..., b_m ( - 10⁹ ≤ b_j ≤ 10⁹) — the coordinates of cellular towers. It is allowed that there are any number of towers in the same point. All coordinates b_j are given in non-decreasing order.

Output

Print minimal r so that each city will be covered by cellular network.

Examples

Input

3 2
-2 2 4
-3 0

Output

4

Input

5 3
1 5 10 14 17
4 11 15

Output

3


题意：在一个数轴上，有n个城市，m个信号塔；给出城市和信号塔的位置，求最小的信号塔影响范围；

   思路：二分答案，check一下就行了；注意爆int；

#include<bits/stdc++.h>
using namespace std;
#define ll __int64
#define esp 0.00000000001
const int N=3e3+10,M=1e6+10,inf=1e9+10,mod=1000000007;
ll a[M];
ll b[M];
int check(ll hh,int x,int y)
{
    int u=1;
    int v=1;
    while(u<=x)
    {
        if(v>y)
        return 0;
        if(a[u]>=b[v]-hh&&b[v]+hh>=a[u])
        u++;
        else
        v++;
    }
    return 1;
}
int main()
{
    int x,y,z,i,t;
    scanf("%d%d",&x,&y);
    for(i=1;i<=x;i++)
    scanf("%I64d",&a[i]);
    for(i=1;i<=y;i++)
    scanf("%I64d",&b[i]);
    sort(a+1,a+1+x);
    sort(b+1,b+1+y);
    ll st=0;
    ll en=2e9;
    while(st<en)
    {
        ll mid=(st+en)>>1;
        if(check(mid,x,y))
        en=mid;
        else
        st=mid+1;
    }
    printf("%I64d
",st);
    return 0;
}