You are given a sequence of n pairs of integers: (a_1, b_1), (a_2, b_2), ... , (a_n, b_n). This sequence is called bad if it is sorted in non-descending order by first elements or if it is sorted in non-descending order by second elements. Otherwise the sequence is good. There are examples of good and bad sequences:

  * s = [(1, 2), (3, 2), (3, 1)] is bad because the sequence of first elements is sorted: [1, 3, 3]; 
  * s = [(1, 2), (3, 2), (1, 2)] is bad because the sequence of second elements is sorted: [2, 2, 2]; 
  * s = [(1, 1), (2, 2), (3, 3)] is bad because both sequences (the sequence of first elements and the sequence of second elements) are sorted; 
  * s = [(1, 3), (3, 3), (2, 2)] is good because neither the sequence of first elements ([1, 3, 2]) nor the sequence of second elements ([3, 3, 2]) is sorted. 



Calculate the number of permutations of size n such that after applying this permutation to the sequence s it turns into a good sequence. 

A permutation p of size n is a sequence p_1, p_2, ... , p_n consisting of n distinct integers from 1 to n (1 ≤ p_i ≤ n). If you apply permutation p_1, p_2, ... , p_n to the sequence s_1, s_2, ... , s_n you get the sequence s_{p_1}, s_{p_2}, ... , s_{p_n}. For example, if s = [(1, 2), (1, 3), (2, 3)] and p = [2, 3, 1] then s turns into [(1, 3), (2, 3), (1, 2)].

Input

The first line contains one integer n (1 ≤ n ≤ 3 ⋅ 10^5).

The next n lines contains description of sequence s. The i-th line contains two integers a_i and b_i (1 ≤ a_i, b_i ≤ n) — the first and second elements of i-th pair in the sequence.

The sequence s may contain equal elements.

Output

Print the number of permutations of size n such that after applying this permutation to the sequence s it turns into a good sequence. Print the answer modulo 998244353 (a prime number).

Examples

Input


3
1 1
2 2
3 1


Output


3


Input


4
2 3
2 2
2 1
2 4


Output


0


Input


3
1 1
1 1
2 3


Output


4

Note

In first test case there are six permutations of size 3: 

  1. if p = [1, 2, 3], then s = [(1, 1), (2, 2), (3, 1)] — bad sequence (sorted by first elements); 
  2. if p = [1, 3, 2], then s = [(1, 1), (3, 1), (2, 2)] — bad sequence (sorted by second elements); 
  3. if p = [2, 1, 3], then s = [(2, 2), (1, 1), (3, 1)] — good sequence; 
  4. if p = [2, 3, 1], then s = [(2, 2), (3, 1), (1, 1)] — good sequence; 
  5. if p = [3, 1, 2], then s = [(3, 1), (1, 1), (2, 2)] — bad sequence (sorted by second elements); 
  6. if p = [3, 2, 1], then s = [(3, 1), (2, 2), (1, 1)] — good sequence. 
import sys
from collections import defaultdict
n=int(sys.stdin.readline())
fact=[0 for _ in range(n+3)]
mod=998244353
fact[0]=1
for i in range(1,n+3):
    fact[i]=fact[i-1]*i%mod
arr=[[0,0] for _ in range(n)]
b=[0 for _ in range(n)]
for _ in range(n):
    u,v=map(int,sys.stdin.readline().split())
    arr[_][0],arr[_][1]=u,v
    b[_]=v
b.sort()
#print(arr,'arr')
arr.sort()
z=True
for i in range(n):
    if b[i]!=arr[i][1]:
        z=False
#print(arr,'aftersort')
lasta,lastb=arr[0][0],arr[0][1]
counta,countc=1,1
la,lb,lc=[],[],[]
bl=b[0]
cb=1
#print(z,'z')
for i in range(1,n):
    if z:
        if arr[i][0]==lasta and arr[i][1]==lastb:
            countc+=1
        else:
            lc.append(countc)
            countc=1
    if arr[i][0]==lasta:
        counta+=1
    else:
        la.append(counta)
        counta=1
        lasta=arr[i][0]
    if b[i]==bl:
        cb+=1
    else:
        lb.append(cb)
        cb=1
        bl=b[i]
    if arr[i][1]==lastb:
        #countb+=1
        pass
    else:
        #lb.append(countb)
        #countb=1
        lastb=arr[i][1]
la.append(counta)
lb.append(cb)
if z:
    lc.append(countc)
#print(la,'la')
#print(lb,'lb')
#print(lc,'lc')
ans=fact[n]
suba,subb,addc=0,0,0
if len(la)>0:
    suba=1
if len(lb)>0:
    subb=1
if len(lc)>0:
    addc=1
for i in range(len(la)):
    suba=suba*fact[la[i]]%mod
for i in range(len(lb)):
    subb=subb*fact[lb[i]]%mod
for i in range(len(lc)):
    addc=addc*fact[lc[i]]%mod
#print(ans,'ans')
ans=(ans%mod-suba%mod-subb%mod+addc%mod)
print(ans%mod)
