Buggy python submission (verdict: Time Limit Exceeded):
N = int(input())
Xmi, Xma, Ymi, Yma, DYmi, DYma, UYmi, UYma, RXmi, RXma, LXmi, LXma = [(10**10), -(10**10)] * 6
for _ in range(N):
    x, y, d = input().split()
    x, y = int(x), int(y)
    
    if d == "R":
        RXmi = min(RXmi, x)
        RXma = max(RXma, x)
    elif d == "L":
        LXmi = min(LXmi, x)
        LXma = max(LXma, x)
    else:
        Xmi = min(Xmi, x)
        Xma = max(Xma, x)
        
    if d == "U":
        UYmi = min(UYmi, y)
        UYma = max(UYma, y)
    elif d == "D":
        DYmi = min(DYmi, y)
        DYma = max(DYma, y)
    else:
        Ymi = min(Ymi, y)
        Yma = max(Yma, y)

def calc(t):
    xmi = min(RXmi+t, LXmi-t, Xmi)
    xma = max(RXma+t, LXma-t, Xma)
    ymi = min(UYmi+t, DYmi-t, Ymi)
    yma = max(UYma+t, DYma-t, Yma)
    return max(yma-ymi, 0)*max(xma-xmi, 0)

mi = 10**20
import random
import time
sTime = time.time()
while time.time()-sTime < 4.5:
    l = 0
    r = 10**(random.randrange(10000)/1000)
    for _ in range(100):
        m1 = (l*2+r)/3
        m2 = (l+r*2)/3
        if calc(m1) > calc(m2):
            l = m1
        else:
            r = m2
    mi = min(mi, calc(m1))


print(mi)

Fixed submission:
from decimal import *
getcontext().prec = 100
N = int(input())
Xmi, Xma, Ymi, Yma, DYmi, DYma, UYmi, UYma, RXmi, RXma, LXmi, LXma = [(10**10), -(10**10)] * 6
for _ in range(N):
    x, y, d = input().split()
    x, y = int(x), int(y)
    
    if d == "R":
        RXmi = min(RXmi, x)
        RXma = max(RXma, x)
    elif d == "L":
        LXmi = min(LXmi, x)
        LXma = max(LXma, x)
    else:
        Xmi = min(Xmi, x)
        Xma = max(Xma, x)
        
    if d == "U":
        UYmi = min(UYmi, y)
        UYma = max(UYma, y)
    elif d == "D":
        DYmi = min(DYmi, y)
        DYma = max(DYma, y)
    else:
        Ymi = min(Ymi, y)
        Yma = max(Yma, y)

def calc(t):
    xmi = min(RXmi+t, LXmi-t, Xmi)
    xma = max(RXma+t, LXma-t, Xma)
    ymi = min(UYmi+t, DYmi-t, Ymi)
    yma = max(UYma+t, DYma-t, Yma)
    return max(yma-ymi, 0)*max(xma-xmi, 0)
    
def dii(t):
    a = Decimal("0.00000001")
    return calc(t+a) - calc(t-a)

l = Decimal("0")
r = Decimal("10000000000")
for _ in range(500):
    m = (l+r)/2
    if dii(m) > 0:
        r = m
    else:
        l = m
print(calc(m))

Buggy python submission (verdict: Time Limit Exceeded):
N = int(input())
Xmi, Xma, Ymi, Yma, DYmi, DYma, UYmi, UYma, RXmi, RXma, LXmi, LXma = [(10**10), -(10**10)] * 6
for _ in range(N):
    x, y, d = input().split()
    x, y = int(x), int(y)
    
    if d == "R":
        RXmi = min(RXmi, x)
        RXma = max(RXma, x)
    elif d == "L":
        LXmi = min(LXmi, x)
        LXma = max(LXma, x)
    else:
        Xmi = min(Xmi, x)
        Xma = max(Xma, x)
        
    if d == "U":
        UYmi = min(UYmi, y)
        UYma = max(UYma, y)
    elif d == "D":
        DYmi = min(DYmi, y)
        DYma = max(DYma, y)
    else:
        Ymi = min(Ymi, y)
        Yma = max(Yma, y)

def calc(t):
    xmi = min(RXmi+t, LXmi-t, Xmi)
    xma = max(RXma+t, LXma-t, Xma)
    ymi = min(UYmi+t, DYmi-t, Ymi)
    yma = max(UYma+t, DYma-t, Yma)
    return max(yma-ymi, 0)*max(xma-xmi, 0)

mi = 10**20
mii = -1

for k in [10**4, 10**2, 1, 0.01, 0.0001, 0.000001, 0.00000001]:
    for i in range(-10**6, 10**6):
        j = mii + i * k
        if j < 0:
            continue
        if calc(j) < mi:
            mi = calc(j)
            mii = j
print(mi)


Fixed submission:
from decimal import *
getcontext().prec = 100
N = int(input())
Xmi, Xma, Ymi, Yma, DYmi, DYma, UYmi, UYma, RXmi, RXma, LXmi, LXma = [(10**10), -(10**10)] * 6
for _ in range(N):
    x, y, d = input().split()
    x, y = int(x), int(y)
    
    if d == "R":
        RXmi = min(RXmi, x)
        RXma = max(RXma, x)
    elif d == "L":
        LXmi = min(LXmi, x)
        LXma = max(LXma, x)
    else:
        Xmi = min(Xmi, x)
        Xma = max(Xma, x)
        
    if d == "U":
        UYmi = min(UYmi, y)
        UYma = max(UYma, y)
    elif d == "D":
        DYmi = min(DYmi, y)
        DYma = max(DYma, y)
    else:
        Ymi = min(Ymi, y)
        Yma = max(Yma, y)

def calc(t):
    xmi = min(RXmi+t, LXmi-t, Xmi)
    xma = max(RXma+t, LXma-t, Xma)
    ymi = min(UYmi+t, DYmi-t, Ymi)
    yma = max(UYma+t, DYma-t, Yma)
    return max(yma-ymi, 0)*max(xma-xmi, 0)
    
def dii(t):
    a = Decimal("0.00000001")
    return calc(t+a) - calc(t-a)

l = Decimal("0")
r = Decimal("10000000000")
for _ in range(500):
    m = (l+r)/2
    if dii(m) > 0:
        r = m
    else:
        l = m
print(calc(m))