Problem:
Score: 300 points

Problem Statement

In 2028 and after a continuous growth, AtCoder Inc. finally built an empire with six cities (City 1, 2, 3, 4, 5, 6)!

There are five means of transport in this empire:

Train: travels from City 1 to 2 in one minute. A train can occupy at most A people.

Bus: travels from City 2 to 3 in one minute. A bus can occupy at most B people.

Taxi: travels from City 3 to 4 in one minute. A taxi can occupy at most C people.

Airplane: travels from City 4 to 5 in one minute. An airplane can occupy at most D people.

Ship: travels from City 5 to 6 in one minute. A ship can occupy at most E people.

For each of them, one vehicle leaves the city at each integer time (time 0, 1, 2, ...).

There is a group of N people at City 1, and they all want to go to City 6.

At least how long does it take for all of them to reach there?
You can ignore the time needed to transfer.

Constraints

1 \leq N, A, B, C, D, E \leq 10^{15}

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A
B
C
D
E

Output

Print the minimum time required for all of the people to reach City 6, in minutes.

Sample Input 1

5
3
2
4
3
5

Sample Output 1

7

One possible way to travel is as follows.
First, there are N = 5 people at City 1, as shown in the following image:

In the first minute, three people travels from City 1 to City 2 by train. Note that a train can only occupy at most three people.

In the second minute, the remaining two people travels from City 1 to City 2 by train, and two of the three people who were already at City 2 travels to City 3 by bus. Note that a bus can only occupy at most two people.

In the third minute, two people travels from City 2 to City 3 by train, and another two people travels from City 3 to City 4 by taxi.

From then on, if they continue traveling without stopping until they reach City 6, all of them can reach there in seven minutes.

There is no way for them to reach City 6 in 6 minutes or less.

Sample Input 2

10
123
123
123
123
123

Sample Output 2

5

All kinds of vehicles can occupy N = 10 people at a time.
Thus, if they continue traveling without stopping until they reach City 6, all of them can reach there in five minutes.

Sample Input 3

10000000007
2
3
5
7
11

Sample Output 3

5000000008

Note that the input or output may not fit into a 32-bit integer type.

Solution in JavaScript (node.js v5.12) (judge verdict: Accepted)

"use strict";

function _toConsumableArray(arr) { return _arrayWithoutHoles(arr) || _iterableToArray(arr) || _nonIterableSpread(); }

function _nonIterableSpread() { throw new TypeError("Invalid attempt to spread non-iterable instance"); }

function _arrayWithoutHoles(arr) { if (Array.isArray(arr)) { for (var i = 0, arr2 = new Array(arr.length); i < arr.length; i++) { arr2[i] = arr[i]; } return arr2; } }

function _classCallCheck(instance, Constructor) { if (!(instance instanceof Constructor)) { throw new TypeError("Cannot call a class as a function"); } }

function _defineProperties(target, props) { for (var i = 0; i < props.length; i++) { var descriptor = props[i]; descriptor.enumerable = descriptor.enumerable || false; descriptor.configurable = true; if ("value" in descriptor) descriptor.writable = true; Object.defineProperty(target, descriptor.key, descriptor); } }

function _createClass(Constructor, protoProps, staticProps) { if (protoProps) _defineProperties(Constructor.prototype, protoProps); if (staticProps) _defineProperties(Constructor, staticProps); return Constructor; }

function _toArray(arr) { return _arrayWithHoles(arr) || _iterableToArray(arr) || _nonIterableRest(); }

function _nonIterableRest() { throw new TypeError("Invalid attempt to destructure non-iterable instance"); }

function _iterableToArray(iter) { if (Symbol.iterator in Object(iter) || Object.prototype.toString.call(iter) === "[object Arguments]") return Array.from(iter); }

function _arrayWithHoles(arr) { if (Array.isArray(arr)) return arr; }

function _main() {
  // ----------
  (function (input) {
    var lines = input.split("\n");

    var _splitNum$slice = splitNum(lines).slice(0, 6),
        _splitNum$slice2 = _toArray(_splitNum$slice),
        N = _splitNum$slice2[0],
        ds = _splitNum$slice2.slice(1);

    var dds = ds.map(function (d, i) {
      return {
        d,
        i
      };
    });
    var dds2 = sortByKey(dds.concat(), ["d", "i"]);
    var bottleneck = dds2[0];
    var btime = Math.ceil(N / bottleneck.d);
    console.log(btime + 4);
  })(require("fs").readFileSync("/dev/stdin", "utf8"));

  function splitNum(line) {
    return (Array.isArray(line) ? line : line.split(/\s+/)).map(function (n) {
      return parseInt(n);
    });
  }
  /**
   * Iterates over integers in [start, end).
   */


  /**
   * Sort given array with keys.
   * sortByKey(arr, ['key1', 'key2'])
   * sortByKey(arr, [['key1', -1], 'key2'])
   */
  function sortByKey(arr, keys) {
    if (!Array.isArray(keys)) {
      keys = [keys];
    }

    return arr.sort(function (a, b) {
      var _iteratorNormalCompletion = true;
      var _didIteratorError = false;
      var _iteratorError = undefined;

      try {
        for (var _iterator = keys[Symbol.iterator](), _step; !(_iteratorNormalCompletion = (_step = _iterator.next()).done); _iteratorNormalCompletion = true) {
          var k = _step.value;

          if ("string" === typeof k) {
            var d = a[k] - b[k];

            if (d !== 0) {
              return d;
            }
          } else {
            var _d = a[k[0]] - b[k[0]];

            var sig = k[1] === "desc" ? -1 : k[1] === "asc" ? 1 : Number(k[1]);

            if (_d !== 0) {
              return _d * sig;
            }
          }
        }
      } catch (err) {
        _didIteratorError = true;
        _iteratorError = err;
      } finally {
        try {
          if (!_iteratorNormalCompletion && _iterator.return != null) {
            _iterator.return();
          }
        } finally {
          if (_didIteratorError) {
            throw _iteratorError;
          }
        }
      }

      return 0;
    });
  }
  /**
   * implementation of arbitrary-precision unsigned integer.
   */


  var Longer =
  /*#__PURE__*/
  function () {
    function Longer(value) {
      _classCallCheck(this, Longer);

      // enough for 64bit
      this.data = [0, 0, 0];
      var idx = 0;

      while (value !== 0) {
        this.data[idx] = value % Longer.border;
        value = Math.floor(value / Longer.border);
        idx++;
      }
    }

    _createClass(Longer, [{
      key: "add",
      value: function add(right) {
        var result = new Longer(0);
        var max = Math.max(this.data.length, right.data.length);
        var carry = 0;
        var idx = 0;

        for (; idx < max; idx++) {
          var sum = (this.data[idx] || 0) + (right.data[idx] || 0) + carry;
          result.data[idx] = sum % Longer.border;
          carry = Math.floor(sum / Longer.border);
        }

        if (carry > 0) {
          result.data[idx] = carry;
        }

        return result;
      }
    }, {
      key: "mul",
      value: function mul(right) {
        var result = new Longer(0);

        for (var lidx = 0; lidx < this.data.length; lidx++) {
          for (var ridx = 0; ridx < right.data.length; ridx++) {
            var me = this.data[lidx] * right.data[ridx];
            var tidx = lidx + ridx;
            var value = me;

            while (value > 0) {
              var sum = (result.data[tidx] || 0) + value;
              result.data[tidx] = sum % Longer.border;
              value = Math.floor(sum / Longer.border);
              tidx++;
            }
          }
        }

        return result;
      }
    }, {
      key: "toString",
      value: function toString() {
        var d = this.data.concat().reverse(); // let fsti = d.findIndex(v => v !== 0);

        var fsti = function (arr, pred) {
          for (var i = 0; i < arr.length; i++) {
            if (pred(arr[i], i)) {
              return i;
            }
          }

          return null;
        } // not full polyfill!
        (d, function (v) {
          return v !== 0;
        });

        if (fsti == null) {
          return "0";
        }

        return d.slice(fsti).map(function (v, i) {
          if (i === 0) {
            return String(v);
          } else {
            // return String(v).padStart(Longer.digits, "0");
            return padStart(String(v), Longer.digits, "0");
          }
        }).join("");

        function padStart(str, num, pad) {
          var n = num - str.length;
          var result = "";

          for (var i = 0; i < n; i++) {
            result += pad;
          }

          return result + str;
        }
      }
    }]);

    return Longer;
  }();
  /** digits per element. */


  Longer.digits = 7;
  Longer.border = Math.pow(10, Longer.digits);
  /**
   * Runs a recursive function expressed as a generator function.
   */
  // ----------
}

_main();