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
/**
  * @brief atcoder
  * @author yao
  */
#include <cstdlib>
#include <cstdio>
#include <cctype>
#include <cstring>
#include <utility>
#include <algorithm>
#include <functional>
#include <climits>
#define ft first
#define sd second
#ifdef DBG
#   define dbg_pri(x...) fprintf(stderr,x)
#else
#   define dbg_pri(x...) 0
#   define NDEBUG
#endif //DBG
#include <cassert>

typedef unsigned int uint;
typedef long long int lli;
typedef unsigned long long int ulli;

#define N 262144
#define P ((int)1e9+7)

int p[N];
int a[N], t[N], tm;

void touch(int k)
{
    if(t[k] != tm) a[k] = 0, t[k] = tm;
}

void set_mir(int u, int k)
{
    while(u)
    {
        k = (lli)k*u % P;
        touch(u);
        a[u] = (a[u] + k) % P;
        u>>=1;
    }
}

void dfs_set(int u, int k, int n)
{
    k = (lli)k*u % P;
    if(u >= n) return set_mir(p[u],k);
    int l = u<<1, r = l+1;
    dfs_set(l, k, n);
    dfs_set(r, k, n);
}

int get_mir(int u)
{
    touch(u);
    int res = a[u], k = u, dir;
    while(dir = u&1, u>>=1)
    {
        k = (lli)k*u % P;
        touch(u<<1|(dir^1));
        res = (res + (lli)a[u<<1|(dir^1)] * k) % P;
    }
    return res;
}

int dfs_get(int u, int n)
{
    if(u >= n) return (lli)get_mir(p[u])*u % P;
    int l = u<<1, r = l+1;
    int res = dfs_get(l, n) + dfs_get(r, n);
    return (lli)res*u % P;
}

int dfs(int u, int n)
{
    if(u >= n) return 0;
    int l = u<<1, r = l+1;
    ++tm;
    dfs_set(l, u, n);
    int res = dfs_get(r, n);
    dbg_pri("poi 1: %d %d\n", u, res);
    res = (res + dfs(l,n)) % P;
    res = (res + dfs(r,n)) % P;
    return res;
}

int main()
{
    int h, n;
    scanf("%d", &h), n = 1<<h-1;
    for(int i=n;i<n*2;++i)scanf("%d", &p[i]), p[i]+=n-1;
    int ans = dfs(1,n);
    printf("%d\n", ans);
    return 0;
}
