Standing On The Shoulders

AtCoder

IDabc352_c

Time2000ms

Memory256MB

Difficulty—

There are $N$ giants, named $1$ to $N$. When giant $i$ stands on the ground, their shoulder height is $A_i$, and their head height is $B_i$. You can choose a permutation $(P_1, P_2, \ldots, P_N)$ of $(1, 2, \ldots, N)$ and stack the $N$ giants according to the following rules: * First, place giant $P_1$ on the ground. The giant $P_1$'s shoulder will be at a height of $A_{P_1}$ from the ground, and their head will be at a height of $B_{P_1}$ from the ground. * For $i = 1, 2, \ldots, N - 1$ in order, place giant $P_{i + 1}$ on the shoulders of giant $P_i$. If giant $P_i$'s shoulders are at a height of $t$ from the ground, then giant $P_{i + 1}$'s shoulders will be at a height of $t + A_{P_{i + 1}}$ from the ground, and their head will be at a height of $t + B_{P_{i + 1}}$ from the ground. Find the maximum possible height of the head of the topmost giant $P_N$ from the ground. ## Constraints * $2 \leq N \leq 2 \times 10^5$ * $1 \leq A_i \leq B_i \leq 10^9$ * All input values are integers. ## Input The input is given from Standard Input in the following format: $N$ $A_1$ $B_1$ $A_2$ $B_2$ $\vdots$ $A_N$ $B_N$ [samples]

Samples

Input #1

Output #1

18

If $(P_1, P_2, P_3) = (2, 1, 3)$, then measuring from the ground, giant $2$ has a shoulder height of $5$ and a head height of $8$, giant $1$ has a shoulder height of $9$ and a head height of $15$, and giant $3$ has a shoulder height of $11$ and a head height of $18$.
The head height of the topmost giant from the ground cannot be greater than $18$, so print $18$.

Input #2

Output #2

Input #3

10
690830957 868532399
741145463 930111470
612846445 948344128
540375785 925723427
723092548 925021315
928915367 973970164
563314352 832796216
562681294 868338948
923012648 954764623
691107436 891127278

Output #3

7362669937

API Response (JSON)

{
  "problem": {
    "name": "Standing On The Shoulders",
    "description": {
      "content": "There are $N$ giants, named $1$ to $N$. When giant $i$ stands on the ground, their shoulder height is $A_i$, and their head height is $B_i$. You can choose a permutation $(P_1, P_2, \\ldots, P_N)$ of $",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc352_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ giants, named $1$ to $N$. When giant $i$ stands on the ground, their shoulder height is $A_i$, and their head height is $B_i$.\nYou can choose a permutation $(P_1, P_2, \\ldots, P_N)$ of $...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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