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. 

def naiveSolve():
    
   
    
    return

MOD=998244353
MAX=int(3e5)+5
fact=[1]
for zz in range(1,MAX+1):
    fact.append(((fact[-1]%MOD)*zz%MOD)%MOD) #with MOD
#    fact.append(fact[-1]*zz) #without MOD
def nCr(n,r): #choose, MOD is prime
    num=fact[n]
    den=((fact[r]%MOD)*(fact[n-r]%MOD))%MOD #with MOD
    return ((num%MOD)*pow(den,MOD-2,MOD))%MOD #with MOD
#    den= fact[r]*fact[n-r]# without MOD
#    return num//den # without MOD
def nPr(n,r): #permute, MOD is prime
    num=fact[n]
    den=fact[n-r]
    return ((num%MOD)*pow(den,MOD-2,MOD))%MOD #with MOD
#    return num//den # without MOD

from collections import Counter

def main():
    
    MOD=998244353
    n=int(input())
    
    # cnt number of permutations-number of bad permutations
    arr=[]
    for _ in range(n):
        arr.append(readIntArr())
    
    totalP=fact[n]
    
    # calculate first asc and second asc
    arr.sort()
    fs=0
    ok=True
    for i in range(1,n):
        if arr[i][1]<arr[i-1][1]:
            ok=False
    if ok:
        fs=1
    pf=ps=-1
    cnt=1
    for i in range(n):
        if arr[i]==[pf,ps]:
            cnt+=1
        else:
            fs*=fact[cnt]
            fs%=MOD
            cnt=1
        pf,ps=arr[i]
    fs*=fact[cnt]
    fs%=MOD
    
    # calculate first asc
    f=1
    pf=-1
    cnt=1
    for i in range(n):
        if arr[i][0]==pf:
            cnt+=1
        else:
            f*=fact[cnt]
            f%=MOD
            cnt=1
        pf=arr[i][0]
    f*=fact[cnt]
    f%=MOD
    
    # calculate second asc
    arr.sort(key=lambda x:x[1])
    s=1
    ps=-1
    cnt=1
    for i in range(n):
        if arr[i][1]==ps:
            cnt+=1
        else:
            s*=fact[cnt]
            s%=MOD
            cnt=1
        ps=arr[i][1]
    s*=fact[cnt]
    s%=MOD
    
    badCnts=(f+s-fs+MOD)%MOD
    ans=(totalP-badCnts+MOD)%MOD
    print(ans)
    
    # print('totalP:{} bad:{} f:{} s:{} fs:{}'.format(totalP,badCnts,f,s,fs))
    
    return


import sys
input=sys.stdin.buffer.readline #FOR READING PURE INTEGER INPUTS (space separation ok)
# input=lambda: sys.stdin.readline().rstrip("\r\n") #FOR READING STRING/TEXT INPUTS.

def oneLineArrayPrint(arr):
    print(' '.join([str(x) for x in arr]))
def multiLineArrayPrint(arr):
    print('\n'.join([str(x) for x in arr]))
def multiLineArrayOfArraysPrint(arr):
    print('\n'.join([' '.join([str(x) for x in y]) for y in arr]))
 
def readIntArr():
    return [int(x) for x in input().split()]
# def readFloatArr():
#     return [float(x) for x in input().split()]
 
def makeArr(defaultValFactory,dimensionArr): # eg. makeArr(lambda:0,[n,m])
    dv=defaultValFactory;da=dimensionArr
    if len(da)==1:return [dv() for _ in range(da[0])]
    else:return [makeArr(dv,da[1:]) for _ in range(da[0])]
 
def queryInteractive(i,j):
    print('? {} {}'.format(i,j))
    sys.stdout.flush()
    return int(input())
 
def answerInteractive(ans):
    print('! {}'.format(' '.join([str(x) for x in ans])))
    sys.stdout.flush()
 
inf=float('inf')
MOD=10**9+7
# MOD=998244353

from math import gcd,floor,ceil
 
for _abc in range(1):
    main()
