You are given sequences A and B consisting of non-negative integers.
The lengths of both A and B are N, and the sums of the elements in A and B are equal.
The i-th element in A is A_i, and the i-th element in B is B_i.
Tozan and Gezan repeats the following sequence of operations:
 - If A and B are equal sequences, terminate the process.
 - Otherwise, first Tozan chooses a positive element in A and decrease it by 1.
 - Then, Gezan chooses a positive element in B and decrease it by 1.
 - Then, give one candy to Takahashi, their pet.
Tozan wants the number of candies given to Takahashi until the process is terminated to be as large as possible, while Gezan wants it to be as small as possible.
Find the number of candies given to Takahashi when both of them perform the operations optimally.

-----Constraints-----
 - 1 \leq N \leq 2 × 10^5
 - 0 \leq A_i,B_i \leq 10^9(1\leq i\leq N)
 - The sums of the elements in A and B are equal.
 - All values in input are integers.

-----Input-----
Input is given from Standard Input in the following format:
N
A_1 B_1
:
A_N B_N

-----Output-----
Print the number of candies given to Takahashi when both Tozan and Gezan perform the operations optimally.

-----Sample Input-----
2
1 2
3 2

-----Sample Output-----
2

When both Tozan and Gezan perform the operations optimally, the process will proceed as follows:
 - Tozan decreases A_1 by 1.
 - Gezan decreases B_1 by 1.
 - One candy is given to Takahashi.
 - Tozan decreases A_2 by 1.
 - Gezan decreases B_1 by 1.
 - One candy is given to Takahashi.
 - As A and B are equal, the process is terminated.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'N = int(input())\ndiff_a_b = []\nfor i in range(N):\n  a, b = map(int, input().split())\n  diff_a_b.append([a - b, a, b])\n\ndiff_a_b.sort()\nif diff_a_b[0][0] == 0: # 最初から数列が等しい\n  print(0)\n  return\n\nans = 0\nd = 0\ntemp = 10**10\nfor diff, a, b in diff_a_b:\n  if diff <= 0: # a <= b\n    ans += b\n    d -= diff\n  else:\n    ans += b\n    temp = min(temp, b)\n\nprint(ans - temp)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: