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
mod = 998244353
fact = [1]
for i in range(1, 300001):
    fact.append((fact[-1]*i)%mod)


data = []
num = int(sys.stdin.readline())

l = []
for _ in range(num):
    data.append(tuple([int(i) for i in sys.stdin.readline().split()]))
    l.append(data[-1][1])

ans = 0
# f.sort()
# last = -1
# tot = 1
# run = 0
# for p in f:
#     if p == last:
#         run += 1
#     else:
#         tot = (tot * fact[run])%mod
#         run = 1
#         last = p
# tot = (tot * fact[run])%mod
# ans += tot

l.sort()
last = -1
tot = 1
run = 0
for p in l:
    if p == last:
        run += 1
    else:
        tot = (tot * fact[run])%mod
        run = 1
        last = p
tot = (tot * fact[run])%mod
ans += tot

data.sort()


f = [i[0] for i in data]

last = -1
tot = 1
run = 0
for p in f:
    if p == last:
        run += 1
    else:
        tot = (tot * fact[run])%mod
        run = 1
        last = p
tot = (tot * fact[run])%mod
ans += tot





sor = True
for i in range(num-1):
    if data[i][1] > data[i+1][1]:
        sor = False
        break

if sor:
    last = (-1, -1)
    tot = 1
    run = 0
    for p in data:
        if p == last:
            run += 1
        else:
            tot = (tot * fact[run])%mod
            run = 1
            last = p
    tot = (tot * fact[run])%mod
    # print(tot)

    ans -= tot 
q = fact[num]
print((q - ans)%998244353)


