Inspired by the tv series Stranger Things, bear Limak is going for a walk between two mirror worlds.

There are two perfect binary trees of height H, each with the standard numeration of vertices from 1 to 2^H-1. The root is 1 and the children of x are 2 \cdot x and 2 \cdot x + 1.

Let L denote the number of leaves in a single tree, L = 2^{H-1}.

You are given a permutation P_1, P_2, \ldots, P_L of numbers 1 through L. It describes L special edges that connect leaves of the two trees. There is a special edge between vertex L+i-1 in the first tree and vertex L+P_i-1 in the second tree.

graph for sample1

drawing for the first sample test, permutation P = (2, 3, 1, 4), special edges in green

Let's define product of a cycle as the product of numbers in its vertices. Compute the sum of products of all simple cycles that have exactly two special edges, modulo (10^9+7).

A simple cycle is a cycle of length at least 3, without repeated vertices or edges.

Constraints

* 2 \leq H \leq 18
* 1 \leq P_i \leq L where L = 2^{H-1}
* P_i \neq P_j (so this is a permutation)

Input

Input is given from Standard Input in the following format (where L = 2^{H-1}).


H
P_1 P_2 \cdots P_L


Output

Compute the sum of products of simple cycles that have exactly two special edges. Print the answer modulo (10^9+7).

Examples

Input

3
2 3 1 4


Output

121788


Input

2
1 2


Output

36


Input

5
6 14 15 7 12 16 5 4 11 9 3 10 8 2 13 1


Output

10199246
#include<bits/stdc++.h>
using namespace std;
#define nn 65536*16
#define mod 1000000007
#define int long long 
int h,n,p[nn],ans=0;
int m;int tag[nn];
void move(int x,int road){
	road=road*x%mod;
	tag[x]=(tag[x]+road)%mod;
	if(x/2) move(x/2,road);
}
void clsmove(int x,int road){
	road=road*x%mod;
	tag[x]=0;
	if(x/2) clsmove(x/2,road);
}
void goleft(int x,int l,int road){
	road=road*x%mod;
	if(l==h-1){
	//	cout<<x<<"="<<m<<":"<<p[x-m]+m<<"\n";
		move(p[x-m]+m,road);
	}
	else{
		goleft(x<<1,l+1,road);
		goleft(x<<1|1,l+1,road);
	}
}
void clsleft(int x,int l,int road){
	road=road*x%mod;
	if(l==h-1){
		clsmove(p[x-m]+m,road);
	}
	else{
		clsleft(x<<1,l+1,1);
		clsleft(x<<1|1,l+1,1);
	}
}
void ask(int x,int road){
	if(x==1) return ;
	int y=x^1;
	road=road*x%mod;
	ans=(ans+tag[y]%mod*road%mod*(x/2))%mod;
	if(x/2) ask(x/2,road);
}
void goright(int x,int l,int road){
	road=road*x%mod;
	if(l==h-1){
		ask(p[x-m]+m,road);
	}
	else{
		goright(x<<1,l+1,road);
		goright(x<<1|1,l+1,road);
	}
}
void dfs(int x,int l){
	if(l!=h-1){
		goleft(x<<1,l+1,1);
		goright(x<<1|1,l+1,x);
		clsleft(x<<1,l+1,1);
	//	memset(tag,0,sizeof tag);
		dfs(x<<1,l+1);
		dfs(x<<1|1,l+1);
	}
}
signed main(){
	scanf("%lld",&h);n=(1<<h-1);m=n-1;
	for(int i=1;i<=n;i++) scanf("%lld",&p[i]);
	dfs(1,0);
	printf("%lld\n",(ans%mod+mod)%mod);
	return 0;
}