An ant moves on the real line with constant speed of 1 unit per second. It starts at 0 and always moves to the right (so its position increases by 1 each second).

There are n portals, the i-th of which is located at position x_i and teleports to position y_i < x_i. Each portal can be either active or inactive. The initial state of the i-th portal is determined by s_i: if s_i=0 then the i-th portal is initially inactive, if s_i=1 then the i-th portal is initially active. When the ant travels through a portal (i.e., when its position coincides with the position of a portal): 

  * if the portal is inactive, it becomes active (in this case the path of the ant is not affected); 
  * if the portal is active, it becomes inactive and the ant is instantly teleported to the position y_i, where it keeps on moving as normal. 



How long (from the instant it starts moving) does it take for the ant to reach the position x_n + 1? It can be shown that this happens in a finite amount of time. Since the answer may be very large, compute it modulo 998 244 353.

Input

The first line contains the integer n (1≤ n≤ 2⋅ 10^5) — the number of portals.

The i-th of the next n lines contains three integers x_i, y_i and s_i (1≤ y_i < x_i≤ 10^9, s_i∈\{0,1\}) — the position of the i-th portal, the position where the ant is teleported when it travels through the i-th portal (if it is active), and the initial state of the i-th portal.

The positions of the portals are strictly increasing, that is x_1<x_2<⋅⋅⋅<x_n. It is guaranteed that the 2n integers x_1,   x_2,   ...,   x_n,   y_1,   y_2,   ...,   y_n are all distinct.

Output

Output the amount of time elapsed, in seconds, from the instant the ant starts moving to the instant it reaches the position x_n+1. Since the answer may be very large, output it modulo 998 244 353.

Examples

Input


4
3 2 0
6 5 1
7 4 0
8 1 1


Output


23


Input


1
454971987 406874902 1


Output


503069073


Input


5
243385510 42245605 0
644426565 574769163 0
708622105 208990040 0
786625660 616437691 0
899754846 382774619 0


Output


899754847


Input


5
200000000 100000000 1
600000000 400000000 0
800000000 300000000 0
900000000 700000000 1
1000000000 500000000 0


Output


3511295

Note

Explanation of the first sample: The ant moves as follows (a curvy arrow denotes a teleporting, a straight arrow denotes normal movement with speed 1 and the time spent during the movement is written above the arrow). $$$ 0 \stackrel{6}{\longrightarrow} 6 \leadsto 5 \stackrel{3}{\longrightarrow} 8 \leadsto 1 \stackrel{2}{\longrightarrow} 3 \leadsto 2 \stackrel{4}{\longrightarrow} 6 \leadsto 5 \stackrel{2}{\longrightarrow} 7 \leadsto 4 \stackrel{2}{\longrightarrow} 6 \leadsto 5 \stackrel{4}{\longrightarrow} 9  Notice that the total time is 6+3+2+4+2+2+4=23$$$.

Explanation of the second sample: The ant moves as follows (a curvy arrow denotes a teleporting, a straight arrow denotes normal movement with speed 1 and the time spent during the movement is written above the arrow). $$$ 0 \stackrel{454971987}{\longrightarrow} 454971987 \leadsto 406874902 \stackrel{48097086}{\longrightarrow} 454971988  Notice that the total time is 454971987+48097086=503069073$$$.

Explanation of the third sample: Since all portals are initially off, the ant will not be teleported and will go straight from 0 to x_n+1=899754846+1=899754847.
import java.util.*;
import java.io.*;

public class _1552_F {
    static final long MOD = 998244353;
    public static void main(String[] args) throws IOException {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(System.out);
        int n = Integer.parseInt(in.readLine());
        int[][] portals = new int[n][3];
        for(int i = 0; i < n; i++) {
            StringTokenizer line = new StringTokenizer(in.readLine());
            portals[i][0] = Integer.parseInt(line.nextToken());
            portals[i][1] = Integer.parseInt(line.nextToken());
            portals[i][2] = Integer.parseInt(line.nextToken());
        }
        Arrays.sort(portals, new Comparator<int[]>() {
            @Override
            public int compare(int[] a, int[] b) {
                return a[0] - b[0];
            }
        });
        int[] back = new int[n];
        for(int i = 0; i < n; i++) {
            back[i] = bsearch(portals, portals[i][1]);
        }
        //dp[i][0, 1] = time to reach portal i for the first, last time, assuming every portal is initially active
        long[][] dp = new long[n][2];
        for(int i = 0; i < n; i++) {
            if(i > 0) {
                dp[i][0] = modadd(dp[i - 1][1], modadd(portals[i][0], -portals[i - 1][0]));
            }else {
                dp[i][0] = portals[i][0];
            }
            dp[i][1] = modadd(modadd(dp[i][0], modadd(portals[back[i]][0], -portals[i][1])), modadd(dp[i][0], -dp[back[i]][0]));
        }
        long time = 0;
        for(int i = 0; i < n; i++) {
            int dist = portals[i][0] - (i > 0 ? portals[i - 1][0] : 0);
            time = modadd(time, dist);
            if(portals[i][2] == 1) {
                time = modadd(time, modadd(dp[i][1], -dp[i][0]));
            }
        }
        out.println(time + 1);
        in.close();
        out.close();
    }
    static int bsearch(int[][] portals, int loc) {
        int l = 0;
        int r = portals.length - 1;
        int res = -1;
        while(l <= r) {
            int avg = (l + r) / 2;
            if(portals[avg][0] >= loc) {
                res = avg;
                r = avg - 1;
            }else {
                l = avg + 1;
            }
        }
        return res;
    }
    static long modadd(long a, long b) {
        return (a + b + MOD) % MOD;
    }
}
