Problem: We have a set S of N points in a two-dimensional plane. The coordinates of the i-th point are (x_i, y_i). The N points have distinct x-coordinates and distinct y-coordinates.

For a non-empty subset T of S, let f(T) be the number of points contained in the smallest rectangle, whose sides are parallel to the coordinate axes, that contains all the points in T. More formally, we define f(T) as follows:

* f(T) :=  (the number of integers i (1 \leq i \leq N) such that a \leq x_i \leq b and c \leq y_i \leq d, where a, b, c, and d are the minimum x-coordinate, the maximum x-coordinate, the minimum y-coordinate, and the maximum y-coordinate of the points in T)



Find the sum of f(T) over all non-empty subset T of S. Since it can be enormous, print the sum modulo 998244353.

Constraints

* 1 \leq N \leq 2 \times 10^5
* -10^9 \leq x_i, y_i \leq 10^9
* x_i \neq x_j (i \neq j)
* y_i \neq y_j (i \neq j)
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N
x_1 y_1
:
x_N y_N


Output

Print the sum of f(T) over all non-empty subset T of S, modulo 998244353.

Examples

Input

3
-1 3
2 1
3 -2


Output

13


Input

4
1 4
2 1
3 3
4 2


Output

34


Input

10
19 -11
-3 -12
5 3
3 -15
8 -14
-9 -20
10 -9
0 2
-7 17
6 -6


Output

7222

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
using ll = long long;

#define mod 998244353

// 区間の和を計算するBIT, 1-indexed
struct BIT{
    int size;
    vector<int>value;
    BIT(int N) : value(N+1, 0), size(N) {}

    int sum(int i) {
        int res = 0;
        while (i > 0) {
            res += value[i];
            i -= i & -i; // i = i & (i-1);
        }
        return res;
    }

    void add (int i, int x) {
        while (i <= size) {
            value[i] += x;
            i += i & -i;
        }
    }
};

int main() {
    int N;
    cin >> N;
    vector<int>x(N);
    vector<int>y(N);
    vector<pair<int, int>> elements(N);
    for (int i = 0; i < N; ++i) {
        cin >> x[i] >> y[i];
    }

    // y座標を 1-indexed で圧縮後, x座標でソート
    vector<int> copyY(y);
    sort(copyY.begin(), copyY.end());
    map<int, int> mp;
    for (int i = 0; i < N; ++i) {
        mp[copyY[i]] = i + 1;
    }
    for (int i = 0; i < N; ++i) {
        y[i] = mp[y[i]];
        elements[i] = make_pair(x[i], y[i]);
    }
    sort(elements.begin(), elements.end());

    // 2の累乗計算
    ll modPow[N+1];
    modPow[0] = 1;
    for (int i = 1; i < N+1; ++i) {
        modPow[i] = modPow[i-1] * 2 % mod;
    }

    ll ans = modPow[N] + mod - 1;
    ans %= mod;
    ans = ans * N % mod;

    BIT tree(N);
    sort(y.begin(), y.end());

    for (int i = 0; i < N; ++i) {
        // 左にi個, 右にN-i-1個の点
        int yi = elements[i].second;
        // vector y には自分自身も含まれていることに注意
        auto iter1 = lower_bound(y.begin(), y.end(), yi);
        int low = distance(y.begin(), iter1);
        // 下にlow個, 上にN-low-1個の点

        int lowOver = tree.sum(yi);
        tree.add(yi, 1);

        // 左下にlowOver個, 左上にi-lowOver個の点
        ans = ans + mod + mod + mod + mod;
        ans = ans - modPow[low] - modPow[N-low-1] - modPow[i] - modPow[N-i-1] + 4;
        ans = ans + modPow[lowOver] + modPow[i-lowOver] + modPow[low - lowOver] + modPow[N-low-1-i+lowOver] - 4;
        ans %= mod;
    }
    cout << ans;
    return 0;
}