題干：

It is known that there are?k?fish species in the polar ocean, numbered from?1?to?k. They are sorted by non-decreasing order of their weight, which is a positive number. Let the weight of the?i-th type of fish be?wi, then?0?<?w1?≤?w2?≤?...?≤?wk?holds.

Polar bears Alice and Bob each have caught some fish, and they are guessing who has the larger sum of weight of the fish he/she's caught. Given the type of the fish they've caught, determine whether it is possible that the fish caught by Alice has a?strictly larger?total weight than Bob's. In other words, does there exist a sequence of weights?wi?(not necessary integers), such that the fish caught by Alice has a strictly larger total weight?

Input

The first line contains three integers?n,?m,?k?(1?≤?n,?m?≤?105,?1?≤?k?≤?109)?— the number of fish caught by Alice and Bob respectively, and the number of fish species.

The second line contains?n?integers each from 1 to?k, the list of fish type caught by Alice. The third line contains?m?integers each from 1 to?k, the list of fish type caught by Bob.

Note that one may have caught more than one fish for a same species.

Output

Output "YES" (without quotes) if it is possible, and "NO" (without quotes) otherwise.

Examples

Input

3 3 3 2 2 2 1 1 3

Output

YES

Input

4 7 9 5 2 7 3 3 5 2 7 3 8 7

Output

NO

Note

In the first sample, if?w1?=?1,?w2?=?2,?w3?=?2.5, then Alice has a total of?2?+?2?+?2?=?6weight units, while Bob only has?1?+?1?+?2.5?=?4.5.

In the second sample, the fish that Alice caught is a subset of Bob's. Therefore, the total weight of Bob’s fish is always not less than the total weight of Alice’s fish.

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解題報告：

? ?OAE的典型應用。。。如果一給我機會，那就前面的一筆勾銷就好了。最后 如果我都用完了，，那就GG，否則我就一定能贏。

AC代碼：

#include<cstdio> #include<iostream> #include<algorithm> #include<queue> #include<map> #include<vector> #include<set> #include<string> #include<cmath> #include<cstring> #define ll long long #define pb push_back #define pm make_pair #define fi first #define se second using namespace std; const int MAX = 2e6 + 5; int n,k; int a[MAX],b[MAX]; int main() {ll n,m,k;cin>>n>>m>>k;for(int i = 1; i<=n; i++) scanf("%d",a+i);for(int i = 1; i<=m; i++) scanf("%d",b+i);sort(a+1,a+n+1);sort(b+1,b+m+1);int cur1,cur2;cur1=cur2=1;while(cur1<=n && cur2<=m) {if(a[cur1] <= b[cur2]) cur1++,cur2++;else cur2++;}if(cur1 == n+1) puts("NO");else puts("YES");return 0 ;}

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