Buggy python submission (verdict: Time Limit Exceeded):
characteristic=10**9+7
def plus(input1,input2):
    return (input1+input2)%characteristic
def minus(input1,input2):
    return (input1-input2)%characteristic
def times(input1,input2):
    return (input1*input2)%characteristic
def exponen(input1,input2):
    return pow(input1,input2,characteristic)
def divide(input1,input2):
    return times(input1,exponen(input2,characteristic-2))
N=int(input())
Fact=[1 for i in range(N+1)]
Finv=[1 for i in range(N+1)]
for i in range(1,N+1):
    Fact[i]=times(Fact[i-1],i)
    Finv[i]=divide(1,Fact[i])
ans=0
SGL=[0 for i in range(N)]
for K in range(N):
    if 2*K-N<0:
        continue
    SGL[K]=times(times(Fact[K],Finv[2*K-N]),Fact[K-1])
for K in range(1,N):
    ans=plus(ans,times(SGL[K]-SGL[K-1],K))
print(ans)


Fixed submission:
P=10**9+7
def egcd(a, b):
    (x, lastx) = (0, 1)
    (y, lasty) = (1, 0)
    while b != 0:
        q = a // b
        (a, b) = (b, a % b)
        (x, lastx) = (lastx - q * x, x)
        (y, lasty) = (lasty - q * y, y)
    return (lastx, lasty, a)
def inv(x):
    return egcd(x,P)[0]
N=int(input())
Fact=[0 for i in range(N+1)]
Finv=[0 for i in range(N+1)]
Fact[0]=1
Finv[0]=1
for i in range(N):
    Fact[i+1]=((i+1)*Fact[i])%P
    Finv[i+1]=(Finv[i]*inv(i+1))%P
SGN=[0 for i in range(N)]
ans=0
for k in range(N):
    if 2*k-N>=0:
        SGN[k]=(((Fact[k-1]*Fact[k])%P)*Finv[2*k-N])%P
        ans=(ans+k*(SGN[k]-SGN[k-1]))%P
print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
characteristic=10**9+7
def plus(input1,input2):
    return (input1+input2)%characteristic
def minus(input1,input2):
    return (input1-input2)%characteristic
def times(input1,input2):
    return (input1*input2)%characteristic
'''
def exponen(input1,input2):
    binaryl=list(str(bin(input2))[2:])
    binarysize=len(binaryl)
    binarylist=[int(binaryl[binarysize-1-i]) for i in range(binarysize)]
    modlist=[0 for i in range(binarysize)]
    modlist[0]=input1
    for i in range(1,binarysize):
        modlist[i]=times(modlist[i-1],modlist[i-1])
    answer=1
    for i in range(binarysize):
        if binarylist[i]==1:
            answer=times(answer,modlist[i])
    return answer
'''
def exponen(input1,input2):
    if input2==0:
        return 1
    elif input2%2==0:
        return exponen(times(input1,input1),input2//2)
    else:
        return times(input1,exponen(times(input1,input1),input2//2))

def divide(input1,input2):
    return times(input1,exponen(input2,characteristic-2))
N=int(input())
Fact=[1 for i in range(N+1)]
Finv=[1 for i in range(N+1)]
for i in range(1,N+1):
    Fact[i]=times(Fact[i-1],i)
    Finv[i]=divide(1,Fact[i])
ans=0
SGL=[0 for i in range(N)]
for K in range(N):
    if 2*K-N<0:
        continue
    SGL[K]=times(times(Fact[K],Finv[2*K-N]),Fact[K-1])
for K in range(1,N):
    ans=plus(ans,times(SGL[K]-SGL[K-1],K))
print(ans)


Fixed submission:
P=10**9+7
def egcd(a, b):
    (x, lastx) = (0, 1)
    (y, lasty) = (1, 0)
    while b != 0:
        q = a // b
        (a, b) = (b, a % b)
        (x, lastx) = (lastx - q * x, x)
        (y, lasty) = (lasty - q * y, y)
    return (lastx, lasty, a)
def inv(x):
    return egcd(x,P)[0]
N=int(input())
Fact=[0 for i in range(N+1)]
Finv=[0 for i in range(N+1)]
Fact[0]=1
Finv[0]=1
for i in range(N):
    Fact[i+1]=((i+1)*Fact[i])%P
    Finv[i+1]=(Finv[i]*inv(i+1))%P
SGN=[0 for i in range(N)]
ans=0
for k in range(N):
    if 2*k-N>=0:
        SGN[k]=(((Fact[k-1]*Fact[k])%P)*Finv[2*k-N])%P
        ans=(ans+k*(SGN[k]-SGN[k-1]))%P
print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
P=10**9+7
def egcd(a, b):
    (x, lastx) = (0, 1)
    (y, lasty) = (1, 0)
    while b != 0:
        q = a // b
        (a, b) = (b, a % b)
        (x, lastx) = (lastx - q * x, x)
        (y, lasty) = (lasty - q * y, y)
    return (lastx, lasty, a)
def inv(x):
    return egcd(x,P)[0]
N=int(input())
Fact=[0 for i in range(N+1)]
Finv=[0 for i in range(N+1)]
Fact[0]=1
Finv[0]=1
for i in range(N):
    Fact[i+1]=((i+1)*Fact[i])%P
    Finv[i+1]=(Finv[i]*inv(i+1))%P
SGN=[0 for i in range(N)]
ans=0
for k in range(N):
    if 2*k-N>=0:
        SGN[k]=(((Fact[k-1]*Fact[k])%P)*Finv[2*k-N])%P
        ans=(ans+k*(SGN[k]-SGN[k-1]))%P
print(ans)


Fixed submission:
P=10**9+7
def egcd(a, b):
    (x, lastx) = (0, 1)
    (y, lasty) = (1, 0)
    while b != 0:
        q = a // b
        (a, b) = (b, a % b)
        (x, lastx) = (lastx - q * x, x)
        (y, lasty) = (lasty - q * y, y)
    return (lastx, lasty, a)
def inv(x):
    return egcd(x,P)[0]
N=int(input())
Fact=[0 for i in range(N+1)]
Finv=[0 for i in range(N+1)]
Fact[0]=1
Finv[0]=1
for i in range(N):
    Fact[i+1]=((i+1)*Fact[i])%P
    Finv[i+1]=(Finv[i]*inv(i+1))%P
SGN=[0 for i in range(N)]
ans=0
for k in range(N):
    if 2*k-N>=0:
        SGN[k]=(((Fact[k-1]*Fact[k])%P)*Finv[2*k-N])%P
        ans=(ans+k*(SGN[k]-SGN[k-1]))%P
print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
characteristic=10**9+7
def plus(input1,input2):
    return (input1+input2)%characteristic
def minus(input1,input2):
    return (input1-input2)%characteristic
def times(input1,input2):
    return (input1*input2)%characteristic
def exponen(input1,input2):
    binaryl=list(str(bin(input2))[2:])
    binarysize=len(binaryl)
    binarylist=[int(binaryl[binarysize-1-i]) for i in range(binarysize)]
    modlist=[0 for i in range(binarysize)]
    modlist[0]=input1
    for i in range(1,binarysize):
        modlist[i]=times(modlist[i-1],modlist[i-1])
    answer=1
    for i in range(binarysize):
        if binarylist[i]==1:
            answer=times(answer,modlist[i])
    return answer
def divide(input1,input2):
    return times(input1,exponen(input2,characteristic-2))
N=int(input())
Fact=[1 for i in range(N+1)]
Finv=[1 for i in range(N+1)]
for i in range(1,N+1):
    Fact[i]=times(Fact[i-1],i)
    Finv[i]=divide(1,Fact[i])
ans=0
SGL=[0 for i in range(N)]
for K in range(N):
    if 2*K-N<0:
        continue
    SGL[K]=times(times(Fact[K],Finv[2*K-N]),Fact[K-1])
for K in range(1,N):
    ans=plus(ans,times(SGL[K]-SGL[K-1],K))
print(ans)


Fixed submission:
P=10**9+7
def egcd(a, b):
    (x, lastx) = (0, 1)
    (y, lasty) = (1, 0)
    while b != 0:
        q = a // b
        (a, b) = (b, a % b)
        (x, lastx) = (lastx - q * x, x)
        (y, lasty) = (lasty - q * y, y)
    return (lastx, lasty, a)
def inv(x):
    return egcd(x,P)[0]
N=int(input())
Fact=[0 for i in range(N+1)]
Finv=[0 for i in range(N+1)]
Fact[0]=1
Finv[0]=1
for i in range(N):
    Fact[i+1]=((i+1)*Fact[i])%P
    Finv[i+1]=(Finv[i]*inv(i+1))%P
SGN=[0 for i in range(N)]
ans=0
for k in range(N):
    if 2*k-N>=0:
        SGN[k]=(((Fact[k-1]*Fact[k])%P)*Finv[2*k-N])%P
        ans=(ans+k*(SGN[k]-SGN[k-1]))%P
print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
characteristic=10**9+7
def plus(input1,input2):
    return (input1+input2)%characteristic
def minus(input1,input2):
    return (input1-input2)%characteristic
def times(input1,input2):
    return (input1*input2)%characteristic
def exponen(input1,input2):
    binaryl=list(str(bin(input2))[2:])
    binarysize=len(binaryl)
    binarylist=[int(binaryl[binarysize-1-i]) for i in range(binarysize)]
    modlist=[0 for i in range(binarysize)]
    modlist[0]=input1
    for i in range(1,binarysize):
        modlist[i]=times(modlist[i-1],modlist[i-1])
    answer=1
    for i in range(binarysize):
        if binarylist[i]==1:
            answer=times(answer,modlist[i])
    return answer
def divide(input1,input2):
    return times(input1,exponen(input2,characteristic-2))
N=int(input())
Fact=[1 for i in range(N+1)]
Finv=[1 for i in range(N+1)]
for i in range(1,N+1):
    Fact[i]=times(Fact[i-1],i)
    Finv[i]=divide(Finv[i-1],i)
ans=0
def C(A,B):
    return times(Fact[A],times(Finv[B],Finv[A-B]))
SGL=[0 for i in range(N)]
for K in range(N):
    if 2*K-N<0:
        continue
    SGL[K]=times(times(Fact[K],Fact[K-1]),Finv[2*K-N])
for K in range(1,N):
    ans=plus(ans,times(SGL[K]-SGL[K-1],K))
print(ans)


Fixed submission:
P=10**9+7
def egcd(a, b):
    (x, lastx) = (0, 1)
    (y, lasty) = (1, 0)
    while b != 0:
        q = a // b
        (a, b) = (b, a % b)
        (x, lastx) = (lastx - q * x, x)
        (y, lasty) = (lasty - q * y, y)
    return (lastx, lasty, a)
def inv(x):
    return egcd(x,P)[0]
N=int(input())
Fact=[0 for i in range(N+1)]
Finv=[0 for i in range(N+1)]
Fact[0]=1
Finv[0]=1
for i in range(N):
    Fact[i+1]=((i+1)*Fact[i])%P
    Finv[i+1]=(Finv[i]*inv(i+1))%P
SGN=[0 for i in range(N)]
ans=0
for k in range(N):
    if 2*k-N>=0:
        SGN[k]=(((Fact[k-1]*Fact[k])%P)*Finv[2*k-N])%P
        ans=(ans+k*(SGN[k]-SGN[k-1]))%P
print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
characteristic=10**9+7
def plus(input1,input2):
    return (input1+input2)%characteristic
def minus(input1,input2):
    return (input1-input2)%characteristic
def times(input1,input2):
    return (input1*input2)%characteristic
def exponen(input1,input2):
    binaryl=list(str(bin(input2))[2:])
    binarysize=len(binaryl)
    binarylist=[int(binaryl[binarysize-1-i]) for i in range(binarysize)]
    modlist=[0 for i in range(binarysize)]
    modlist[0]=input1
    for i in range(1,binarysize):
        modlist[i]=times(modlist[i-1],modlist[i-1])
    answer=1
    for i in range(binarysize):
        if binarylist[i]==1:
            answer=times(answer,modlist[i])
    return answer
def divide(input1,input2):
    return times(input1,exponen(input2,characteristic-2))
N=int(input())
Fact=[1 for i in range(N+1)]
for i in range(1,N+1):
    Fact[i]=times(i,Fact[i-1])
ans=0
def C(A,B):
    return divide(Fact[A],times(Fact[B],Fact[A-B]))
SGL=[0 for i in range(N)]
for K in range(N):
    if 2*K-N<0:
        continue
    F=times(Fact[K],Fact[N-1-K])
    G=C(K-1,N-1-K)
    SGL[K]=(times(F,G))
for K in range(1,N):
    ans=plus(ans,times(SGL[K]-SGL[K-1],K))
print(ans)


Fixed submission:
P=10**9+7
def egcd(a, b):
    (x, lastx) = (0, 1)
    (y, lasty) = (1, 0)
    while b != 0:
        q = a // b
        (a, b) = (b, a % b)
        (x, lastx) = (lastx - q * x, x)
        (y, lasty) = (lasty - q * y, y)
    return (lastx, lasty, a)
def inv(x):
    return egcd(x,P)[0]
N=int(input())
Fact=[0 for i in range(N+1)]
Finv=[0 for i in range(N+1)]
Fact[0]=1
Finv[0]=1
for i in range(N):
    Fact[i+1]=((i+1)*Fact[i])%P
    Finv[i+1]=(Finv[i]*inv(i+1))%P
SGN=[0 for i in range(N)]
ans=0
for k in range(N):
    if 2*k-N>=0:
        SGN[k]=(((Fact[k-1]*Fact[k])%P)*Finv[2*k-N])%P
        ans=(ans+k*(SGN[k]-SGN[k-1]))%P
print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
characteristic=10**9+7
def plus(input1,input2):
    return (input1+input2)%characteristic
def minus(input1,input2):
    return (input1-input2)%characteristic
def times(input1,input2):
    return (input1*input2)%characteristic
def exponen(input1,input2):
    binaryl=list(str(bin(input2))[2:])
    binarysize=len(binaryl)
    binarylist=[int(binaryl[binarysize-1-i]) for i in range(binarysize)]
    modlist=[0 for i in range(binarysize)]
    modlist[0]=input1
    for i in range(1,binarysize):
        modlist[i]=times(modlist[i-1],modlist[i-1])
    answer=1
    for i in range(binarysize):
        if binarylist[i]==1:
            answer=times(answer,modlist[i])
    return answer
def divide(input1,input2):
    return times(input1,exponen(input2,characteristic-2))
N=int(input())
Fact=[1 for i in range(N+1)]
for i in range(1,N+1):
    Fact[i]=times(i,Fact[i-1])
ans=0
def C(A,B):
    return divide(Fact[A],times(Fact[B],Fact[A-B]))
SGL=[0 for i in range(N)]
for K in range(N):
    if 2*K-N<0:
        continue
    F=times(Fact[K],Fact[N-1-K])
    G=C(K-1,N-1-K)
    SGL[K]=(times(F,G))
for K in range(1,N):
    ans=plus(ans,times(SGL[K]-SGL[K-1],K))
print(ans)


Fixed submission:
P=10**9+7
def egcd(a, b):
    (x, lastx) = (0, 1)
    (y, lasty) = (1, 0)
    while b != 0:
        q = a // b
        (a, b) = (b, a % b)
        (x, lastx) = (lastx - q * x, x)
        (y, lasty) = (lasty - q * y, y)
    return (lastx, lasty, a)
def inv(x):
    return egcd(x,P)[0]
N=int(input())
Fact=[0 for i in range(N+1)]
Finv=[0 for i in range(N+1)]
Fact[0]=1
Finv[0]=1
for i in range(N):
    Fact[i+1]=((i+1)*Fact[i])%P
    Finv[i+1]=(Finv[i]*inv(i+1))%P
SGN=[0 for i in range(N)]
ans=0
for k in range(N):
    if 2*k-N>=0:
        SGN[k]=(((Fact[k-1]*Fact[k])%P)*Finv[2*k-N])%P
        ans=(ans+k*(SGN[k]-SGN[k-1]))%P
print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
import itertools
P=10**9+7
N=int(input())
S=list(itertools.permutations(range(N-1),N-1))
scoresum=0
for sg in S:
    score=0
    L=[0 for i in range(N)]
    W=N
    for i in range(N-1):
        if L[sg[i]]==0:
            W-=1
        L[sg[i]]=1
        if L[sg[i]+1]==0:
            W-=1
        L[sg[i]+1]=1
        if W==0:
            score=i+1
            break
    scoresum+=score
print(scoresum)


Fixed submission:
P=10**9+7
def egcd(a, b):
    (x, lastx) = (0, 1)
    (y, lasty) = (1, 0)
    while b != 0:
        q = a // b
        (a, b) = (b, a % b)
        (x, lastx) = (lastx - q * x, x)
        (y, lasty) = (lasty - q * y, y)
    return (lastx, lasty, a)
def inv(x):
    return egcd(x,P)[0]
N=int(input())
Fact=[0 for i in range(N+1)]
Finv=[0 for i in range(N+1)]
Fact[0]=1
Finv[0]=1
for i in range(N):
    Fact[i+1]=((i+1)*Fact[i])%P
    Finv[i+1]=(Finv[i]*inv(i+1))%P
SGN=[0 for i in range(N)]
ans=0
for k in range(N):
    if 2*k-N>=0:
        SGN[k]=(((Fact[k-1]*Fact[k])%P)*Finv[2*k-N])%P
        ans=(ans+k*(SGN[k]-SGN[k-1]))%P
print(ans)