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 increasing(arr):
    n = len(arr)
    for i in range(n-1):
        if arr[i+1][0] < arr[i][0] or arr[i+1][1] < arr[i][1]:
            return False

    return True

def getFacts(n,mod):
    facts = [1]*n
    for i in range(1,n):
        facts[i] = facts[i-1]*i
        facts[i] %= mod

    return facts

def solve(arr1,arr2,n,mod):
    facts = getFacts(4*10**5+1,mod)
    total = facts[n]
    dist1 = {}
    for i in arr1:
        if i[0] not in dist1.keys():
            dist1[i[0]] = 1
        else:
            dist1[i[0]] += 1

    dist2 = {}
    for i in arr2:
        if i[0] not in dist2.keys():
            dist2[i[0]] = 1
        else:
            dist2[i[0]] += 1

    count = 1
    for i in dist1:
        count *= facts[dist1[i]]
        count = count%mod

    total -= count
    count = 1
    
    for i in dist2:
        count *= facts[dist2[i]]
        count = count%mod

    #print(count)
    total -= count

    arr1.sort()
    if increasing(arr1):
        count = 1
    else:
        count = 0
    dist3 = {}
    for i in arr1:
        if i not in dist3.keys():
            dist3[i] = 1
        else:
            dist3[i] += 1
        
    for i in dist3:
        count *= facts[dist3[i]]
        count = count%mod

    #print(count,total)
    total += count
    total = total%mod
    print(total)
    

def main():
    mod = 998244353
    n = int(input())
    first = []
    second = []
    for i in range(n):
        a,b = map(int,input().split())
        first.append((a,b))
        second.append((b,a))
    
    solve(first,second,n,mod)


main()
