Buggy python submission (verdict: Time Limit Exceeded):
def sum_lr(l, r, cnt):
    cnt += 1
    lr = l + r
    if lr < 10:
        l = lr
        return l, cnt
    else:
        l = lr // 10
        r = lr % 10
        return sum_lr(l, r, cnt)

from collections import defaultdict
aaa = defaultdict(lambda:{})
for l in range(10):
    for r in range(10):
        aaa[l][r] = sum_lr(l,r,0)
        

def dc_compression(d, c, ret, cnt):
    if c == 1:
        ret.append((d, 1))
        return ret, cnt
    
    if c % 2 == 1:
        ret.append((d, 1))
        c -= 1
    d, tmp_cnt = aaa[d][d]
    c = c // 2
    cnt += tmp_cnt * c
    #print(d, c, ret, cnt)
    return dc_compression(d, c, ret, cnt)
    
    
    
        

M = int(input())

nums = []
l = 0
cnt = 0
import sys
input = sys.stdin.readline
for _ in range(M):
    d, c = map(int, input().split())
    tmp_nums, tmp_cnt= dc_compression(d,c,[], 0)
    nums += tmp_nums
    cnt += tmp_cnt
    
#print(nums)    
    
for d, c in nums:
    l, tmp_cnt = aaa[l][d]
    cnt += tmp_cnt

print(cnt-1)

Fixed submission:
def sum_lr(l, r, cnt):
    cnt += 1
    lr = l + r
    if lr < 10:
        l = lr
        return l, cnt
    else:
        l = lr // 10
        r = lr % 10
        return sum_lr(l, r, cnt)

from collections import defaultdict
aaa = defaultdict(lambda:{})
for l in range(10):
    for r in range(10):
        aaa[l][r] = sum_lr(l,r,0)
        

def dc_compression(d, c, ret, cnt):
    if c == 1:
        ret.append((d, 1))
        return ret, cnt
    
    if c % 2 == 1:
        ret.append((d, 1))
        c -= 1
    d, tmp_cnt = aaa[d][d]
    c = c // 2
    cnt += tmp_cnt * c
    #print(d, c, ret, cnt)
    return dc_compression(d, c, ret, cnt)
    
    
    
        

M = int(input())

nums = []
l = 0
cnt = 0
import sys
input = sys.stdin.readline
for _ in range(M):
    d, c = map(int, input().split())
    tmp_nums, tmp_cnt= dc_compression(d,c,[], 0)
    for t,_ in tmp_nums:
        nums.append(t)
    
    cnt += tmp_cnt
    
#print(nums)    
    
for d in nums:
    l, tmp_cnt = aaa[l][d]
    cnt += tmp_cnt

print(cnt-1)

Buggy python submission (verdict: Time Limit Exceeded):

def sum_lr(l, r, cnt):
    cnt += 1
    lr = l + r
    if lr < 10:
        l = lr
        return l, cnt
    else:
        l = lr // 10
        r = lr % 10
        return sum_lr(l, r, cnt)

def dc_compression(d, c, ret, cnt):
    if c == 1:
        ret.append((d, 1))
        return ret, cnt
    
    if c % 2 == 1:
        ret.append((d, 1))
        c -= 1
    d, tmp_cnt = sum_lr(d, d, 0)
    c = c // 2
    cnt += tmp_cnt * c
    #print(d, c, ret, cnt)
    return dc_compression(d, c, ret, cnt)
    
    
    
        

M = int(input())

nums = []
l = 0
cnt = 0
import sys
input = sys.stdin.readline
for _ in range(M):
    d, c = map(int, input().split())
    tmp_nums, tmp_cnt= dc_compression(d,c,[], 0)
    nums += tmp_nums
    cnt += tmp_cnt
    
for d, c in nums:
    for _ in range(c):
        l, tmp_cnt = sum_lr(l,d,0)
        cnt += tmp_cnt

print(cnt-1)

Fixed submission:
def sum_lr(l, r, cnt):
    cnt += 1
    lr = l + r
    if lr < 10:
        l = lr
        return l, cnt
    else:
        l = lr // 10
        r = lr % 10
        return sum_lr(l, r, cnt)

from collections import defaultdict
aaa = defaultdict(lambda:{})
for l in range(10):
    for r in range(10):
        aaa[l][r] = sum_lr(l,r,0)
        

def dc_compression(d, c, ret, cnt):
    if c == 1:
        ret.append((d, 1))
        return ret, cnt
    
    if c % 2 == 1:
        ret.append((d, 1))
        c -= 1
    d, tmp_cnt = aaa[d][d]
    c = c // 2
    cnt += tmp_cnt * c
    #print(d, c, ret, cnt)
    return dc_compression(d, c, ret, cnt)
    
    
    
        

M = int(input())

nums = []
l = 0
cnt = 0
import sys
input = sys.stdin.readline
for _ in range(M):
    d, c = map(int, input().split())
    tmp_nums, tmp_cnt= dc_compression(d,c,[], 0)
    for t,_ in tmp_nums:
        nums.append(t)
    
    cnt += tmp_cnt
    
#print(nums)    
    
for d in nums:
    l, tmp_cnt = aaa[l][d]
    cnt += tmp_cnt

print(cnt-1)

Buggy python submission (verdict: Time Limit Exceeded):

def sum_lr(l, r, cnt):
    cnt += 1
    lr = l + r
    if lr < 10:
        l = lr
        return l, cnt
    else:
        l = lr // 10
        r = lr % 10
        return sum_lr(l, r, cnt)

def dc_compression(d, c, ret, cnt):
    if c == 1:
        ret.append((d, 1))
        return ret, cnt
    
    if c % 2 == 1:
        ret.append((d, 1))
        c -= 1
    d, tmp_cnt = sum_lr(d, d, 0)
    c = c // 2
    cnt += tmp_cnt * c
    #print(d, c, ret, cnt)
    return dc_compression(d, c, ret, cnt)
    
    
    
        

M = int(input())

nums = []
l = 0
cnt = 0
for _ in range(M):
    d, c = map(int, input().split())
    tmp_nums, tmp_cnt= dc_compression(d,c,[], 0)
    nums += tmp_nums
    cnt += tmp_cnt
    
for d, c in nums:
    for _ in range(c):
        l, tmp_cnt = sum_lr(l,d,0)
        cnt += tmp_cnt

print(cnt-1)

Fixed submission:
def sum_lr(l, r, cnt):
    cnt += 1
    lr = l + r
    if lr < 10:
        l = lr
        return l, cnt
    else:
        l = lr // 10
        r = lr % 10
        return sum_lr(l, r, cnt)

from collections import defaultdict
aaa = defaultdict(lambda:{})
for l in range(10):
    for r in range(10):
        aaa[l][r] = sum_lr(l,r,0)
        

def dc_compression(d, c, ret, cnt):
    if c == 1:
        ret.append((d, 1))
        return ret, cnt
    
    if c % 2 == 1:
        ret.append((d, 1))
        c -= 1
    d, tmp_cnt = aaa[d][d]
    c = c // 2
    cnt += tmp_cnt * c
    #print(d, c, ret, cnt)
    return dc_compression(d, c, ret, cnt)
    
    
    
        

M = int(input())

nums = []
l = 0
cnt = 0
import sys
input = sys.stdin.readline
for _ in range(M):
    d, c = map(int, input().split())
    tmp_nums, tmp_cnt= dc_compression(d,c,[], 0)
    for t,_ in tmp_nums:
        nums.append(t)
    
    cnt += tmp_cnt
    
#print(nums)    
    
for d in nums:
    l, tmp_cnt = aaa[l][d]
    cnt += tmp_cnt

print(cnt-1)

Buggy python submission (verdict: Time Limit Exceeded):
l = 0
cnt = 0
def sum_lr(r):
    global l
    global cnt
    cnt += 1
    lr = l + r
    if lr < 10:
        l = lr
    else:
        l = lr // 10
        r = lr % 10
        sum_lr(r)


M = int(input())

nums = []
for _ in range(M):
    d, c = map(int, input().split())
    nums.append((d,c))
    
for d, c in nums:
    for _ in range(c):
        sum_lr(d)

print(cnt-1)

Fixed submission:
def sum_lr(l, r, cnt):
    cnt += 1
    lr = l + r
    if lr < 10:
        l = lr
        return l, cnt
    else:
        l = lr // 10
        r = lr % 10
        return sum_lr(l, r, cnt)

from collections import defaultdict
aaa = defaultdict(lambda:{})
for l in range(10):
    for r in range(10):
        aaa[l][r] = sum_lr(l,r,0)
        

def dc_compression(d, c, ret, cnt):
    if c == 1:
        ret.append((d, 1))
        return ret, cnt
    
    if c % 2 == 1:
        ret.append((d, 1))
        c -= 1
    d, tmp_cnt = aaa[d][d]
    c = c // 2
    cnt += tmp_cnt * c
    #print(d, c, ret, cnt)
    return dc_compression(d, c, ret, cnt)
    
    
    
        

M = int(input())

nums = []
l = 0
cnt = 0
import sys
input = sys.stdin.readline
for _ in range(M):
    d, c = map(int, input().split())
    tmp_nums, tmp_cnt= dc_compression(d,c,[], 0)
    for t,_ in tmp_nums:
        nums.append(t)
    
    cnt += tmp_cnt
    
#print(nums)    
    
for d in nums:
    l, tmp_cnt = aaa[l][d]
    cnt += tmp_cnt

print(cnt-1)